3060 Static Bars and Ladders.ipynb

{
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   "cell_type": "markdown",
   "id": "4774a8b6-06ab-4dff-a029-0d39655b5dcb",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
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"
    }
   },
   "cell_type": "markdown",
   "id": "a5fac7db-4d9f-4383-af66-e59be028a103",
   "metadata": {},
   "source": [
    "![image.png](attachment:058dc4d9-4772-4f0b-9fb2-60065d38e228.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5feca8bb-e729-4e84-97f1-c0ba0c0b36dc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5618a620-24f7-415d-b7d0-d4ad0113928a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e1=\\int \\left(t^{3} - 9 t^{2} + 10\\right)\\, dt$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1=MyIntg(t**3-9*t**2+10,'e1',var=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "5d2cac82-d454-4d65-95f1-0ff2d585d80d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\int \\left(t^{3} - 9 t^{2} + 10\\right)\\, dt$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q=MQI(x,e1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e2892b92-b2e0-4020-b0c0-e6dc1468a2ab",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = C_{1} + \\frac{t^{4}}{4} - 3 t^{3} + 10 t$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q.doit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b952a8db-0a05-4fdc-825b-32aa35aaece8",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle C1 =94$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x = \\frac{t^{4}}{4} - 3 t^{3} + 10 t + 94$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C1=Q.solve('C1','update',x=6,t=4)"
   ]
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "c7e08373-d4e0-4001-8377-4035a9bd37a5",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "attachments": {
    "91ea4501-3849-427f-aa08-9fe0bcf5defa.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "6ba99f9e-5727-4280-9904-03c83ff3e127",
   "metadata": {},
   "source": [
    "![image.png](attachment:91ea4501-3849-427f-aa08-9fe0bcf5defa.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "b877e8ca-200d-4192-b656-945d1b39b7e3",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *\n",
    "from lib_Mechanics import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ef85b871-823d-45fa-b245-606375d04b3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x' = 2 \\sin{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "P="
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "e082584d-39e2-463d-acde-7033a0edb3ef",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x =C_{1} - \\cos{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=Q1.dsolve('F')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "5b3e1d74-adb6-4786-b75e-853ad73ee1b2",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle x =- \\cos{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle C1 =0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C1=x.solve('C1','update',x=-1,t=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "22098f99-423d-4098-a87b-56d5df010c9b",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle dx =2 \\sin{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d2x =4 \\cos{\\left(2 t \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dx=x.diff(t,'dx')\n",
    "d2x=x.diff(t,t,'d2x')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "56806b74-5d1c-4290-9d28-f3b49372ca23",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y' = 4 t$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Q2=MyEqDiff(\"y'\",\"4*t\",t,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "4b665fb9-909f-4ac1-b102-dedc0176042c",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y =C_{1} + 2 t^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y=Q2.dsolve('F')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c1953788-6281-4661-aa0d-c04ecbf62ff9",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle y =2 t^{2}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle C1 =0$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "C1=y.solve('C1','update',y=-0,t=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "2e94ea07-0ddf-484f-b504-0c2a2498cb86",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle dy =4 t$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle d2y =4$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dy=y.diff(t,'dy')\n",
    "d2y=y.diff(t,t,'d2y')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "a429280a-78e0-4145-ab0c-5f1052e7de0f",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "alpha1=atan(dy/dx) \n",
    "alpha2=atan(d2y/d2x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "868c61f6-99e7-4722-9f65-6dfa7162f57d",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle \\sqrt{16 \\cos^{2}{\\left(2 t \\right)} + 16}$"
      ],
      "text/plain": [
       "   ___________________\n",
       "  ╱       2           \n",
       "╲╱  16⋅cos (2⋅t) + 16 "
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=sqrt(d2y()**2+d2x()**2)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "42209be0-899b-4cbd-9fab-496ee39441d5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle at =\\sqrt{16 \\cos^{2}{\\left(2 t \\right)} + 16} \\cos{\\left(\\operatorname{atan}{\\left(\\frac{2 t}{\\sin{\\left(2 t \\right)}} \\right)} - \\operatorname{atan}{\\left(\\frac{1}{\\cos{\\left(2 t \\right)}} \\right)} \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "at=MyEq(a*cos(alpha1-alpha2),'at',var=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "e37aa725-698c-45c3-93d9-2ce0411f0793",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 4.06826977118219$"
      ],
      "text/plain": [
       "4.068269771182187"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(at(8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "63aad34e-bf2a-4702-97e2-e4553d256d8f",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle an =- \\sqrt{16 \\cos^{2}{\\left(2 t \\right)} + 16} \\sin{\\left(\\operatorname{atan}{\\left(\\frac{2 t}{\\sin{\\left(2 t \\right)}} \\right)} - \\operatorname{atan}{\\left(\\frac{1}{\\cos{\\left(2 t \\right)}} \\right)} \\right)}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "an=MyEq(a*sin(alpha2-alpha1),'an',var=t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "60e6802d-7f7f-46de-809d-4961c5f6beee",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/latex": [
       "$\\displaystyle 3.75805374534975$"
      ],
      "text/plain": [
       "3.758053745349754"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "float(an(8))"
   ]
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "6e5de242-4b18-4508-8b2b-c67cf348a95b",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "attachments": {
    "91ea4501-3849-427f-aa08-9fe0bcf5defa.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "00cd4cdc-bc21-4b13-a397-12b0b4cd9b80",
   "metadata": {},
   "source": [
    "![image.png](attachment:91ea4501-3849-427f-aa08-9fe0bcf5defa.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c512835f-365a-4754-8aec-021b02a1c71b",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98095651-6d27-4581-b85b-2c33e59afa38",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "063c7b36-1669-4acd-9680-3586d47a2e4e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "47be5fd8-34de-40ab-b7e1-fc1d83753a59",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "attachments": {
    "91ea4501-3849-427f-aa08-9fe0bcf5defa.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "91cf4647-b833-4185-83b3-632a25b81ec1",
   "metadata": {},
   "source": [
    "![image.png](attachment:91ea4501-3849-427f-aa08-9fe0bcf5defa.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "04a8d4bd-7125-4254-a30a-b3e7edbafffc",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "3d4ee03c-f896-479a-9e50-5b311b43745e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "42c357f8-d00c-4e63-92fd-970a33873554",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "attachments": {
    "baddecb4-e838-40d2-b5f0-cf399d0f02ce.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAABUoAAAAECAIAAADXt5J4AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAAAAzSURBVHhe7dcBCQAACAMw2zym0TXHYbASm9sAAAAA1fQeAAAA6uk9AAAA1NN7AAAAKLd5jCnMx9KfoBcAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "id": "dea8a1db-0450-4503-b788-27a7c8bd74de",
   "metadata": {
    "tags": []
   },
   "source": [
    "![line.png](attachment:baddecb4-e838-40d2-b5f0-cf399d0f02ce.png)"
   ]
  },
  {
   "attachments": {
    "91ea4501-3849-427f-aa08-9fe0bcf5defa.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "id": "c4516bb5-287d-4abd-9cda-981e6cffca4e",
   "metadata": {},
   "source": [
    "![image.png](attachment:91ea4501-3849-427f-aa08-9fe0bcf5defa.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5a08fcbc-10d5-4a1a-860f-152ed29d631e",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from Libaldomath import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ab7eb733-25d0-43fd-8924-35a2dc4d6a3a",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5066fc95-a54d-40ab-9365-3adf32ee0577",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}