diff --git a/15 Advance Rigid Boddy.ipynb b/15 Advance Rigid Boddy.ipynb deleted file mode 100644 index 1be139f..0000000 --- a/15 Advance Rigid Boddy.ipynb +++ /dev/null @@ -1,2005 +0,0 @@ -{ - "cells": [ - { - "attachments": { - "2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII=" - } - }, - "cell_type": "markdown", - "id": "d0a91d73-ddd4-41bb-9b0c-56fe62014084", - "metadata": {}, - "source": [ - "![line.png](attachment:2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "id": "c9df797a-2e45-4ac1-9491-2de3a85c9550", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "from physic_lib2 import * # run this to reset all variablesmm=from physic_lib2 import * # run this to reset all variables" - ] - }, - { - "attachments": { - "721a2966-30a4-454c-bc4d-e425d2c679f0.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "b09152ee-64cb-4c90-b004-40def9b34acf", - "metadata": {}, - "source": [ - "![e13_100.png](attachment:721a2966-30a4-454c-bc4d-e425d2c679f0.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "id": "6fe12606-353d-4f1d-91ef-1e8f8a11bd4f", - "metadata": {}, - "outputs": [], - "source": [ - "A=mparticle()\n", - "A.addF((F,0),(m*g,-pi/2-alpha),(N1,pi/2),(f1,pi))\n", - "B=mparticle()\n", - "B.addF((f1,0),(2*m*g,-pi/2-alpha),(N1,-pi/2),(N2,pi/2),(f2,pi))" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "id": "5b7cab53-d09c-42c0-9dc3-bd0982cc29b5", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle f1 =N_{1} \\mu_{1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle f2 =N_{2} \\mu_{2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "f1=MyEq(N1*mu1,'f1')\n", - "f2=MyEq(N2*mu2,'f2')" - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "id": "87d2f788-e228-438a-aa7a-255064e7f787", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Fy =N_{1} - g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle N1 =g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Fya=FyQ(A)\n", - "N1=Fya.ssolve('N1')" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "id": "0d556a6a-0873-438e-8d60-5dfc0219064d", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Fx =F - f_{1} - g m \\sin{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Fxa=FxQ(A)" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "id": "5e53c32a-a6cb-4a15-8df7-10cd553cf510", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle N1 =g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle f1 =g m \\mu_{1} \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle f2 =N_{2} \\mu_{2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle Fx =F - g m \\mu_{1} \\cos{\\left(\\alpha \\right)} - g m \\sin{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Upgrade(N1,N2,f1,f2,Fxa)" - ] - }, - { - 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" - } - }, - "cell_type": "markdown", - "id": "913141fe-2a66-4715-9aaa-c0e8463a569b", - "metadata": {}, - "source": [ - "![imagen.png](attachment:53b518fd-4965-4e58-97ab-c29847c4e0f0.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "id": "145bdd6e-f5bc-429a-be9c-78ddfb29265c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle F =g m \\left(\\mu_{1} \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "F=Fxa.ssolve('F')" - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "id": "ecb85127-1953-487d-a8e8-34987f68a379", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Fy =- N_{1} + N_{2} - 2 g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Fyb=FyQ(B)" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "id": "dbd62c1d-5b42-4660-85e3-7c63bf4690ec", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle N2 =N_{1} + 2 g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N2=Fyb.ssolve('N2')" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "id": "8d0cb710-3583-4c39-aa33-1f0a7648c97a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle N1 =g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle N2 =3 g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle f1 =g m \\mu_{1} \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle f2 =3 g m \\mu_{2} \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle Fx =- g m \\mu_{1} \\cos{\\left(\\alpha \\right)} + g m \\left(\\mu_{1} \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right) - g m \\sin{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle F =g m \\left(\\mu_{1} \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Upgrade(N1,N2,f1,f2,Fxa,Fyb,F)" - ] - }, - { - "attachments": { - "2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "122095b9-b0c4-4a96-a016-a510459fe9ae", - "metadata": {}, - "source": [ - "![e13_200.png](attachment:60635d24-8052-4fc2-a5a6-258eabdd1df9.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "id": "b312eca0-bac9-4bc1-8ff7-4db793d3a0a3", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "from physic_lib2 import * # run this to reset all variables" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "id": "fe01f2e9-c328-47a2-b6df-25e1bbbd9a3b", - "metadata": {}, - "outputs": [], - "source": [ - "# create and adding forzas with pos to use torque\n", - "\n", - "fr1=r1*mu\n", - "fr2=r2*mu\n", - "A=mparticle(m=m,g=g)\n", - "A.addF((r2,pi/2),(fr2,0),(4*m*g,-pi/2,2*L*sin(alpha),2*L*cos(alpha)),(m*g,-pi/2,2*L*cos(alpha)-L/2,2*L*sin(alpha)))\n", - "A.addF((r1,pi,4*L*cos(alpha),4*L*sin(alpha)),(fr1,pi/2,4*L*cos(alpha),4*L*sin(alpha)))" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "id": "f129a127-165b-4e1e-b01e-c6ac4081ec1f", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Fx =\\mu r_{2} - r_{1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle Fy =- 5 g m + \\mu r_{1} + r_{2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Fx=FxQ(A,kope='x')\n", - "Fy=FyQ(A,kope='x') # = cero" - ] - }, - { - "attachments": { - "64572766-414a-4d94-8c09-924a2a119f84.png": { - "image/png": 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- } - }, - "cell_type": "markdown", - "id": "38677eae-4a21-44fd-b401-925d661305d0", - "metadata": {}, - "source": [ - "![imagen.png](attachment:64572766-414a-4d94-8c09-924a2a119f84.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "id": "a9c329e2-a366-4c1d-9690-3a71d4abad14", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle r1 =\\frac{5 g m \\mu}{\\mu^{2} + 1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle r2 =\\frac{5 g m}{\\mu^{2} + 1}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "r1,r1=solvelin(Fx,Fy,r1,r2) # return MyEq " - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "id": "db937593-c05f-466b-98e0-524f46cfb8f4", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =8 L g m \\sin{\\left(\\alpha \\right)} - 4 L \\mu r_{1} \\cos{\\left(\\alpha \\right)} - 4 L r_{1} \\sin{\\left(\\alpha \\right)} + g m \\left(2 L \\cos{\\left(\\alpha \\right)} - \\frac{L}{2}\\right)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To=ToQ(A) " - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "id": "1a4494ca-0ba8-43af-890c-23aa7506c633", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =8 L g m \\sin{\\left(\\alpha \\right)} + g m \\left(2 L \\cos{\\left(\\alpha \\right)} - \\frac{L}{2}\\right)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.set('r1',0)" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "id": "c38a2c0e-f450-4b99-a8b6-05a12bfa315e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =16 \\sin{\\left(\\alpha \\right)} + 4 \\cos{\\left(\\alpha \\right)} - 1$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.reduFac()" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "id": "d92e6728-899c-43c4-ac1c-30959648efde", - "metadata": {}, - "outputs": [], - "source": [ - "#little help because sympy hurt asterisk when try whit angles.." - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "id": "b32bc802-cb0a-4eee-a9c6-74180397683e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[-1, 4*cos(alpha), 16*sin(alpha)]" - ] - }, - "execution_count": 19, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "To.list() # args list to see what choise..." - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "id": "f1ab4a93-643e-4631-8a82-2671afe2f567", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle 4 \\cos{\\left(\\alpha \\right)} = 16 \\sin{\\left(\\alpha \\right)} - 1$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ToQ=To.toEqual([1])" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "id": "9d777521-b53a-4027-b9f9-0039cd8c7cc7", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\cos{\\left(\\alpha \\right)} = 4 \\sin{\\left(\\alpha \\right)} - \\frac{1}{4}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ToQ.Div(4)" - ] - }, - { - "cell_type": "code", - "execution_count": 22, - "id": "95e9ed31-a558-450d-96ad-db5b23e35190", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\cos^{2}{\\left(\\alpha \\right)} = \\left(4 \\sin{\\left(\\alpha \\right)} - \\frac{1}{4}\\right)^{2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ToQ.Pow(2)" - ] - }, - { - "cell_type": "code", - "execution_count": 23, - "id": "6884ab1b-505b-4a0e-8a56-13a8e3c6be1e", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle \\cos^{2}{\\left(\\alpha \\right)} = 16 \\sin^{2}{\\left(\\alpha \\right)} - 2 \\sin{\\left(\\alpha \\right)} + \\frac{1}{16}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ToQ.expand()" - ] - }, - { - "cell_type": "code", - "execution_count": 24, - "id": "e1c5746f-739e-4579-9c4d-23671f94674f", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle 1 - \\sin^{2}{\\left(\\alpha \\right)} = 16 \\sin^{2}{\\left(\\alpha \\right)} - 2 \\sin{\\left(\\alpha \\right)} + \\frac{1}{16}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "ToQ.cos2sin(alpha)" - ] - }, - { - "cell_type": "code", - "execution_count": 25, - "id": "67cddfad-f975-4200-9e33-b7f5f5e02a5a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =- 17 \\sin^{2}{\\left(\\alpha \\right)} + 2 \\sin{\\left(\\alpha \\right)} + \\frac{15}{16}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To=ToQ.toMyEq('To')" - ] - }, - { - "cell_type": "code", - "execution_count": 26, - "id": "ec9f6d18-be3a-4b15-82c8-de0d2d20da70", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =- 272 \\sin^{2}{\\left(\\alpha \\right)} + 32 \\sin{\\left(\\alpha \\right)} + 15$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.reduFac()" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "id": "5c06b218-7828-4a7f-a282-4f9d813974e9", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle sA =0.300912906369917$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "sA=To.solve(sin(alpha),'sA',korden=1,kope='N') " - ] - }, - { - "cell_type": "code", - "execution_count": 77, - "id": "d4a9494a-d55e-48c7-996f-ef152137df32", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle α =17.5124426389433$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "alpha=MyEq(rad2sex(asin(sA)),alphaname('alpha'))" - ] - }, - { - "cell_type": "code", - "execution_count": 29, - "id": "dd9ed7f5-efd0-4a5a-a379-6e383fe2d8af", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'ß'" - ] - }, - "execution_count": 29, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "alphaname(beta) " - ] - }, - { - "cell_type": "code", - "execution_count": 30, - "id": "2764b932-935e-47ca-a898-1284d322b640", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "'θ'" - ] - }, - "execution_count": 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" - } - }, - "cell_type": "markdown", - "id": "ff459347-41b1-4aa5-98d4-23ae1f94e886", - "metadata": {}, - "source": [ - "![e13_300.png](attachment:6bfa6c98-0f0e-4509-9967-cd4c3bfcd941.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 31, - "id": "9a96d316-ce3a-4ac7-ae78-754b58f5f9d0", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "from physic_lib2 import * # run this to reset all variables" - ] - }, - { - "cell_type": "code", - "execution_count": 32, - "id": "6f50ca8c-7aba-4597-943b-6664c90b1d57", - "metadata": {}, - "outputs": [], - "source": [ - "P=mparticle()" - ] - }, - { - "cell_type": "code", - "execution_count": 33, - "id": "c47c84ff-e8b5-4e3a-93cc-bb2c429515f2", - "metadata": {}, - "outputs": [], - "source": [ - "P.addF((m*g,-pi/2-alpha,L/2,0),(N1,pi/2,L+x,0),(N2,-pi/2,L+x+d,0),(N1*mu,0,L+x,0),(N2*mu,0,L+x+d,0))" - ] - }, - { - "cell_type": "code", - "execution_count": 34, - "id": "5f578c20-7cef-4f29-bed6-3ae2b7920217", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Fx =N_{1} \\mu + N_{2} \\mu - g m \\sin{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle Fy =N_{1} - N_{2} - g m \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle To =\\frac{L g m \\cos{\\left(\\alpha \\right)}}{2} - N_{1} \\left(L + x\\right) + N_{2} \\left(L + d + x\\right)$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Fx=FxQ(P);Fy=FyQ(P);To=ToQ(P) # = cero" - ] - }, - { - "cell_type": "code", - "execution_count": 35, - "id": "b7e2be6e-cc53-482f-a40b-491a1c29b5a5", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle N1 =\\frac{g m \\cos{\\left(\\alpha \\right)}}{2} + \\frac{g m \\sin{\\left(\\alpha \\right)}}{2 \\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle N2 =- \\frac{g m \\cos{\\left(\\alpha \\right)}}{2} + \\frac{g m \\sin{\\left(\\alpha \\right)}}{2 \\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N1,N2=solvelin(Fx,Fy,N1,N2)" - ] - }, - { - "cell_type": "code", - "execution_count": 36, - "id": "72ab7030-fcd4-4387-ac05-62f0159e4857", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =\\frac{g m \\left(- L \\mu \\cos{\\left(\\alpha \\right)} - d \\mu \\cos{\\left(\\alpha \\right)} + d \\sin{\\left(\\alpha \\right)} - 2 \\mu x \\cos{\\left(\\alpha \\right)}\\right)}{2 \\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle N1 =\\frac{g m \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{2 \\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle N2 =\\frac{g m \\left(- \\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{2 \\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Upgrade(To,N1,N2,kope='s')" - ] - }, - { - "cell_type": "code", - "execution_count": 37, - "id": "c5fb5a39-419f-420c-a420-3cd947ad5b2a", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =L \\mu \\cos{\\left(\\alpha \\right)} + d \\mu \\cos{\\left(\\alpha \\right)} - d \\sin{\\left(\\alpha \\right)} + 2 \\mu x \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.reduFac() " - ] - }, - { - "cell_type": "code", - "execution_count": 38, - "id": "9c260978-d9ef-4d97-a308-98b87bdac181", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =L \\mu + d \\mu - \\frac{d \\sin{\\left(\\alpha \\right)}}{\\cos{\\left(\\alpha \\right)}} + 2 \\mu x$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.Div(cos(alpha))" - ] - }, - { - "cell_type": "code", - "execution_count": 39, - "id": "22825033-6a34-4e58-97c5-13808ba52fbc", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =L \\mu + d \\mu - d \\tan{\\left(\\alpha \\right)} + 2 \\mu x$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.tsimplify()" - ] - }, - { - "cell_type": "code", - "execution_count": 40, - "id": "4c0cdce5-9024-4313-98a8-09b1e80eda4b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle x =\\frac{- L \\mu - d \\mu + d \\tan{\\left(\\alpha \\right)}}{2 \\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "x=To.ssolve(x)" - ] - }, - { - "attachments": { - "2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII=" - } - }, - "cell_type": "markdown", - "id": "02ab5940-4707-4c0d-8418-63dfa4352431", - "metadata": {}, - "source": [ - "![line.png](attachment:2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png)" - ] - }, - { - "attachments": { - "8fe81986-89ef-4d51-b0ff-1de2168fba13.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "2f56c7fc-ba8a-40c3-ab00-1ede823a6fb8", - "metadata": {}, - "source": [ - "![e13_400.png](attachment:8fe81986-89ef-4d51-b0ff-1de2168fba13.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 41, - "id": "8cc72c62-47d0-4a9c-b143-a97687a8476c", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "from physic_lib2 import * # run this to reset all variables" - ] - }, - { - "cell_type": "code", - "execution_count": 42, - "id": "9e0c5e18-44ec-441f-9e54-04dee2d7ac27", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle N1 =\\frac{3 g m}{\\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "N1=eQsolve(N1*mu*r-m*g*3*r,'N1')" - ] - }, - { - "cell_type": "code", - "execution_count": 43, - "id": "0e2571ba-2d28-47ee-bcdc-93c2a4693647", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle e2 =- g m + \\frac{3 g m \\cos{\\left(\\alpha \\right)}}{\\mu}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "e2=e2Q(N1*cos(alpha)-m*g)" - ] - }, - { - "cell_type": "code", - "execution_count": 44, - "id": "9216527d-18b7-4e07-b747-f0ed24c5258c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle cos(α) =\\frac{\\mu}{3}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "cA=e2.solve(cos(alpha),alphaname('calpha'))" - ] - }, - { - "attachments": { - "2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII=" - } - }, - "cell_type": "markdown", - "id": "8e927be6-1db0-4a1a-a2c6-685456ed8048", - "metadata": {}, - "source": [ - 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" - } - }, - "cell_type": "markdown", - "id": "c045f44a-3d64-4481-b585-8e88457d0eba", - "metadata": {}, - "source": [ - "![imagen.png](attachment:896b0132-4427-41c5-9f9c-138aa21de318.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 45, - "id": "3009f233-33c0-4202-ac55-d7362735c036", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "from physic_lib2 import * # run this to reset all variables" - ] - }, - { - "cell_type": "code", - "execution_count": 46, - "id": "c0216cc6-d7fe-47f1-9874-c3d8bdccdedc", - "metadata": {}, - "outputs": [], - "source": [ - "P=mparticle(m=m,g=g,y1=0,y2=L/2,v1=0,w1=0)\n", - "P.add_Inerce(M,L,L/2,'r')\n", - "P.add_forza(M*g,-pi/2,L*cos(alpha)/2,-L*sin(alpha)/2)" - ] - }, - { - "attachments": { - "f4e4208c-59ce-4d3f-8414-8b7564f77d4b.png": { - "image/png": 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" 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"execution_count": 49, - "id": "0413961a-2631-4ae9-9ade-470dec1e23d0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle a_t =\\frac{3 g \\cos{\\left(\\alpha \\right)}}{2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "at=eQrot(P,andsolve='at')" - ] - }, - { - "cell_type": "code", - "execution_count": 50, - "id": "306a2b1d-b4a6-440f-8a84-4b0451a08e93", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle e1 =\\frac{L^{2} M w_{2}^{2}}{6} - \\frac{L M g}{2}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "e1=e1Q(P.energia('P')+P.energia_rot())" - ] - }, - { - "cell_type": "code", - "execution_count": 51, - "id": "22748e03-e8da-4532-8221-5e45ba9bd97c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle w2 =\\sqrt{3} \\sqrt{\\frac{g}{L}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "w2=e1.ssolveR('w2')" - ] - }, - { - "attachments": { - "2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png": { - "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII=" - } - }, - "cell_type": "markdown", - "id": "7bcbac5a-2b37-436a-9639-ce13dd8be6c8", - "metadata": {}, - "source": [ - "![line.png](attachment:2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png)" - ] - }, - { - "attachments": { - "7e8aa5c0-355f-472d-8738-fc19024a87ca.png": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "id": "69b621ec-4bca-42be-9cac-f8595961b326", - "metadata": {}, - "source": [ - "![imagen.png](attachment:7e8aa5c0-355f-472d-8738-fc19024a87ca.png)" - ] - }, - { - "cell_type": "code", - "execution_count": 52, - "id": "596c14c3-7e77-4cda-a461-5f975292a985", - "metadata": { - "tags": [] - }, - "outputs": [], - "source": [ - "from physic_lib2 import * # run this to reset all variables\n", - "x1=-R*cos(alpha+tetha)\n", - "x2=R*cos(tetha-alpha)\n", - "y1=-R*sin(alpha+tetha)\n", - "y2=-R*sin(tetha-alpha)" - ] - }, - { - "cell_type": "code", - "execution_count": 53, - "id": "1f2a925e-cd38-4af5-a7d8-62c27c477539", - "metadata": {}, - "outputs": [], - "source": [ - "P1=mparticle()\n", - "P1.add_forza(k*m*g,-pi/2)\n", - "P1.add_forza(F1,alpha+tetha)\n", - "P1.add_forza(Nm,pi-alpha)" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "id": "0b6ce25b-1287-4d74-9e53-ecb37a6c21ba", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Fx1 =F_{1} \\cos{\\left(\\alpha + \\theta \\right)} - Nm \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle Fy1 =F_{1} \\sin{\\left(\\alpha + \\theta \\right)} + Nm \\sin{\\left(\\alpha \\right)} - g k m$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Fx1=FxQ(P1,'Fx1')\n", - "Fy1=FyQ(P1,'Fy1')" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "id": "04fa53a4-d082-4e33-8d2e-ae3da0b3b463", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Nm =\\frac{g k m \\cos{\\left(\\alpha + \\theta \\right)}}{\\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha + \\theta \\right)} + \\sin{\\left(\\alpha + \\theta \\right)} \\cos{\\left(\\alpha \\right)}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle F1 =\\frac{g k m \\cos{\\left(\\alpha \\right)}}{\\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha + \\theta \\right)} + \\sin{\\left(\\alpha + \\theta \\right)} \\cos{\\left(\\alpha \\right)}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Nm,F1=solvelin(Fx1,Fy1,Nm,F1)" - ] - }, - { - "cell_type": "code", - "execution_count": 56, - "id": "6fad00af-55de-4e43-8ad5-1a0c421c696e", - "metadata": {}, - "outputs": [], - "source": [ - "P2=mparticle()\n", - "P2.add_forza(m*g,-pi/2)\n", - "P2.add_forza(F2,pi-tetha+alpha)\n", - "P2.add_forza(Nm,alpha)" - ] - }, - { - "cell_type": "code", - "execution_count": 57, - "id": "06f4a4f2-d9cf-4756-a141-74cb70203fec", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle Fx2 =- F_{2} \\cos{\\left(\\alpha - \\theta \\right)} + \\frac{g k m \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\alpha + \\theta \\right)}}{\\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha + \\theta \\right)} + \\sin{\\left(\\alpha + \\theta \\right)} \\cos{\\left(\\alpha \\right)}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - }, - { - "data": { - "text/latex": [ - "$\\displaystyle Fy2 =- F_{2} \\sin{\\left(\\alpha - \\theta \\right)} + \\frac{g k m \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha + \\theta \\right)}}{\\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha + \\theta \\right)} + \\sin{\\left(\\alpha + \\theta \\right)} \\cos{\\left(\\alpha \\right)}} - g m$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Fx2=FxQ(P2,'Fx2')\n", - "Fy2=FyQ(P2,'Fy2')" - ] - }, - { - "cell_type": "code", - "execution_count": 58, - "id": "5c1c3622-1f8d-4441-824a-5eafa2980b37", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle F2 =\\frac{g k m \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\alpha + \\theta \\right)}}{\\sin{\\left(2 \\alpha + \\theta \\right)} \\cos{\\left(\\alpha - \\theta \\right)}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "F2=Fx2.ssolve('F2')" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "id": "550364a3-c57a-4711-b443-b89f79d960bb", - "metadata": {}, - "outputs": [], - "source": [ - "P=mparticle()\n", - "P.add_forza(k*m*g,-pi/2,x1,y1)\n", - "P.add_forza(F1,alpha+tetha,x1,y1)\n", - "P.add_forza(m*g,-pi/2,x2,y2)\n", - "P.add_forza(F2,pi-tetha+alpha,x2,y2)" - ] - }, - { - "cell_type": "code", - "execution_count": 60, - "id": "cc289374-0763-4a87-bf35-d51abff181b2", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =- R g k m \\cos{\\left(\\alpha + \\theta \\right)} + R g m \\cos{\\left(\\alpha - \\theta \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To=ToQ(P)" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "id": "29087490-366a-4bc4-835c-696ceb25baac", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =k \\cos{\\left(\\alpha + \\theta \\right)} - \\cos{\\left(\\alpha - \\theta \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.reduFac()" - ] - }, - { - "cell_type": "code", - "execution_count": 62, - "id": "56c9419e-0578-4d45-a7d2-c999cb258ae2", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =k \\left(- \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\theta \\right)} + \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)}\\right) - \\sin{\\left(\\alpha \\right)} \\sin{\\left(\\theta \\right)} - \\cos{\\left(\\alpha \\right)} \\cos{\\left(\\theta \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.texpand()" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "id": "660a1299-71c7-41b6-a582-28c75462ad10", - "metadata": {}, - "outputs": [], - "source": [ - "T3=MyTriang(hipo=R,cat2=L/2)" - ] - }, - { - "cell_type": "code", - "execution_count": 64, - "id": "8d414d8f-5fa2-4007-830e-ce8f50127b11", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =- \\frac{L \\cos{\\left(\\alpha \\right)}}{2 R} + k \\left(\\frac{L \\cos{\\left(\\alpha \\right)}}{2 R} - \\frac{\\sqrt{- \\frac{L^{2}}{4} + R^{2}} \\sin{\\left(\\alpha \\right)}}{R}\\right) - \\frac{\\sqrt{- \\frac{L^{2}}{4} + R^{2}} \\sin{\\left(\\alpha \\right)}}{R}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.upTriang(tetha,T3)" - ] - }, - { - "cell_type": "code", - "execution_count": 65, - "id": "ea46dc8b-f981-45a9-8a37-5ffd2f7497e2", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =\\frac{L k \\cos{\\left(\\alpha \\right)}}{2 R} - \\frac{L \\cos{\\left(\\alpha \\right)}}{2 R} - \\frac{k \\sqrt{- \\frac{L^{2}}{4} + R^{2}} \\sin{\\left(\\alpha \\right)}}{R} - \\frac{\\sqrt{- \\frac{L^{2}}{4} + R^{2}} \\sin{\\left(\\alpha \\right)}}{R}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.expand()" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "id": "e6d973b2-48a3-48b0-b439-46caf818fbe0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =\\frac{L k \\cos{\\left(\\alpha \\right)} - L \\cos{\\left(\\alpha \\right)} - k \\sqrt{- L^{2} + 4 R^{2}} \\sin{\\left(\\alpha \\right)} - \\sqrt{- L^{2} + 4 R^{2}} \\sin{\\left(\\alpha \\right)}}{2 R}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.factor()" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "id": "27c20ee2-4023-4dd9-a136-73d7d5375e5c", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =L k \\cos{\\left(\\alpha \\right)} - L \\cos{\\left(\\alpha \\right)} - k \\sqrt{- L^{2} + 4 R^{2}} \\sin{\\left(\\alpha \\right)} - \\sqrt{- L^{2} + 4 R^{2}} \\sin{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.reduFac()" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "id": "0f933b4c-d13b-41c0-b378-3f2e20a47056", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =- k \\sqrt{- L^{2} + 4 R^{2}} \\sin{\\left(\\alpha \\right)} - \\sqrt{- L^{2} + 4 R^{2}} \\sin{\\left(\\alpha \\right)} + \\left(L k - L\\right) \\cos{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.factorSec(cos(alpha))" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "id": "f9545266-03a7-497f-89fd-ced66165d7c5", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =\\left(L k - L\\right) \\cos{\\left(\\alpha \\right)} + \\left(- k \\sqrt{- L^{2} + 4 R^{2}} - \\sqrt{- L^{2} + 4 R^{2}}\\right) \\sin{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.factorSec(sin(alpha))" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "id": "ff44f366-ac54-4852-8a47-bbfea1570291", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =L k - L + \\frac{\\left(- k \\sqrt{- L^{2} + 4 R^{2}} - \\sqrt{- L^{2} + 4 R^{2}}\\right) \\sin{\\left(\\alpha \\right)}}{\\cos{\\left(\\alpha \\right)}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.Div(cos(alpha))" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "112bdbb7-77a1-4d43-ac8f-9fc12adbba20", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle To =L k - L + \\left(- k \\sqrt{- L^{2} + 4 R^{2}} - \\sqrt{- L^{2} + 4 R^{2}}\\right) \\tan{\\left(\\alpha \\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "To.tsimplify()" - ] - }, - { - "cell_type": "code", - "execution_count": 72, - "id": "662f17dd-e22a-4098-8dfc-7af1042c15a6", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle tan(α) =\\frac{L \\left(k - 1\\right)}{\\sqrt{- L^{2} + 4 R^{2}} \\left(k + 1\\right)}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Ta=To.solve(tan(alpha),alphaname('talpha'))" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "id": "63f15817-3638-43d5-bb5c-9de0bb71ef82", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle tan(α) =\\frac{\\sqrt{3} R \\left(k - 1\\right)}{\\left(3 k + 3\\right) \\sqrt{R^{2}}}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Ta.set(L,R)" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "id": "fa71fcc6-e249-4c63-a0ae-727af3c9199b", - "metadata": {}, - "outputs": [ - { - "data": { - "text/latex": [ - "$\\displaystyle tan(α) =\\frac{\\sqrt{3} \\left(k - 1\\right)}{3 k + 3}$" - ], - "text/plain": [ - "" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "Ta.killSimpleRoot()" - ] - }, - { - "attachments": { - "2d984d64-4ed1-4ebe-be12-a4b1e9039eee.png": { - "image/png": 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