5220 Body Slides Rotating Conical Surface.ipynb

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   "id": "440d166c",
   "metadata": {
    "tags": []
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   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
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"
    }
   },
   "cell_type": "markdown",
   "id": "04a5d40f",
   "metadata": {},
   "source": [
    "![dedic.png](attachment:c9fff4c9-2c42-4f2f-9214-9bfc1d497739.png)"
   ]
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "259455f1-add4-4217-91cd-c476d4ea741b",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5036e200-da97-4f27-8a2e-dfce5548ee46",
   "metadata": {},
   "outputs": [],
   "source": [
    "# mu=0"
   ]
  },
  {
   "attachments": {
    "5b53b83f-b31d-4b90-a1b3-3017eb77d4f0.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "b4407ccb-19ae-40ce-898d-7fdcaec3909a",
   "metadata": {},
   "source": [
    "![image.png](attachment:5b53b83f-b31d-4b90-a1b3-3017eb77d4f0.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3bbf5a54-9ebf-44aa-961d-7d135ae2d74c",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "2d71baca-a357-46d3-b469-8489256228fa",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P=phybody()\n",
    "x1=x*cos(alpha)\n",
    "y1=x*sin(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "08cdc0d7-0653-4a11-9784-ff11a5a2831d",
   "metadata": {},
   "outputs": [],
   "source": [
    "P.add_forza(m*g,-pi/2,x1,y1)\n",
    "P.add_forza(N1,alpha+pi/2,x1,y1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a4cd97d5-d9fa-4d0c-8948-9d7658326b7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fy =N_{1} \\cos{\\left(\\alpha \\right)} - g m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fy=P.Fy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "27bcebb2-9b15-450c-aa13-309633dac9d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - m r w^{2} = - N_{1} \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR=P.eQmovradial()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "066412f0-c605-4468-a4a3-5d3556b85b31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m r w^{2} = N_{1} \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "d28f64d9-84be-4514-a30f-99b69fe0820e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m w^{2} x \\cos{\\left(\\alpha \\right)} = N_{1} \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.set(r=x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c21ebe74-8846-443d-ac9d-4e6e44cbe1b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle m w^{2} x \\cos{\\left(\\alpha \\right)} = \\frac{g m \\sin{\\left(\\alpha \\right)}}{\\cos{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.set(N1=Fy.solve(N1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "431c2e14-ae46-4af9-af54-63223850c4ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{g \\sin{\\left(\\alpha \\right)}}{w^{2} \\cos^{2}{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.alone(x)"
   ]
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "5e119b86-cddc-4c0f-9ab4-3a0790f1ddcf",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b641be86-612a-4736-a265-de5b3f99d592",
   "metadata": {},
   "outputs": [],
   "source": [
    "# mu != 0"
   ]
  },
  {
   "attachments": {
    "aed01f58-008b-4fd8-ac75-af16acb1929d.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "77668bec-4595-4e14-ad14-d2eb2b3fda75",
   "metadata": {},
   "source": [
    "![image.png](attachment:aed01f58-008b-4fd8-ac75-af16acb1929d.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "9214371e-ed6a-4495-832b-b7c569b823be",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cd0ca564-7078-4c7e-8aaf-bf035abc0a40",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "P=phybody()\n",
    "x1=x*cos(alpha)\n",
    "y1=x*sin(alpha)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "6fa4a2fb-c6a9-4d1e-b97d-e5f6e2a5634a",
   "metadata": {},
   "outputs": [],
   "source": [
    "P.add_forza(m*g,-pi/2,x1,y1)\n",
    "P.add_forza(N1,alpha+pi/2,x1,y1)\n",
    "P.add_forza(fr,alpha+pi,x1,y1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "387a3c54-56f6-40dc-a200-35c26755ce06",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fy =N_{1} \\cos{\\left(\\alpha \\right)} - f_{r} \\sin{\\left(\\alpha \\right)} - g m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fy=P.Fy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c595cbf8-6931-48a9-90af-fcac7d700f34",
   "metadata": {},
   "outputs": [],
   "source": [
    "P.set(fr,N1*mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "d27abe3c-83c2-4bc9-982f-b48f5a5230d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fy =- N_{1} \\mu \\sin{\\left(\\alpha \\right)} + N_{1} \\cos{\\left(\\alpha \\right)} - g m$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fy=P.Fy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "28331a28-cce0-4245-a5e5-fe1cebc9c726",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle - m r w^{2} = - N_{1} \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR=P.eQmovradial()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e80fc7d2-8de5-464a-9d0d-b7a4ff4c6cd2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle r w^{2} = \\frac{N_{1} \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.simplify()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0ec39c9a-ab8a-4380-bb95-fc912139f03a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle w^{2} x \\cos{\\left(\\alpha \\right)} = \\frac{N_{1} \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{m}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.set(r=x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ccb7eb2c-f667-4075-a6a6-e68e10e7ab23",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle w^{2} x \\cos{\\left(\\alpha \\right)} = \\frac{g \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{- \\mu \\sin{\\left(\\alpha \\right)} + \\cos{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.set(N1=Fy.solve(N1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b4eb7e22-acd1-4f68-bf2a-b6d1ee622743",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{2 g \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{w^{2} \\left(- \\mu \\sin{\\left(2 \\alpha \\right)} + \\cos{\\left(2 \\alpha \\right)} + 1\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.alone(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "3b716b2d-224a-45e3-a303-47a28edccdcf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{2 g \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{w^{2} \\left(- 2 \\mu \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha \\right)} + 2 \\cos^{2}{\\left(\\alpha \\right)}\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.texpand()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "b2892e65-d103-4c9b-b8ba-4006e74298c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{2 g \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{w^{2} \\left(- 2 \\mu \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha \\right)} - 2 \\sin^{2}{\\left(\\alpha \\right)} + 2\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.subs((cos(alpha))**2,(1-sin(alpha)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "b4a84a4c-65d6-41cf-8032-3ab9b46c43d1",
   "metadata": {
    "jupyter": {
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = - \\frac{g \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{w^{2} \\left(\\mu \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha \\right)} + \\sin^{2}{\\left(\\alpha \\right)} - 1\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3e4c614e-da97-4e70-b598-87f88c89164b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = - \\frac{g \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{w^{2} \\left(\\mu \\sin{\\left(\\alpha \\right)} \\cos{\\left(\\alpha \\right)} - \\cos^{2}{\\left(\\alpha \\right)}\\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.subs((sin(alpha))**2,(1-cos(alpha)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5309411c-51fc-4921-89f1-86d977082514",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{g \\left(\\mu \\cos{\\left(\\alpha \\right)} + \\sin{\\left(\\alpha \\right)}\\right)}{w^{2} \\left(- \\mu \\sin{\\left(\\alpha \\right)} + \\cos{\\left(\\alpha \\right)}\\right) \\cos{\\left(\\alpha \\right)}}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "eR.factor()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "0305f786-fac9-449d-af36-a49284432aab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fxy =- N_{1} \\mu - g m \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fxy=P.fxrelative(alpha,'Fxy')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "93701ca1-2838-435e-84df-5fa63ff99282",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle Fxy =- \\frac{g m \\mu}{- \\mu \\sin{\\left(\\alpha \\right)} + \\cos{\\left(\\alpha \\right)}} - g m \\sin{\\left(\\alpha \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fxy.set(N1=Fy.solve(N1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e31ff150-5833-41a3-96f6-6ec776bfd6ea",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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