Merge branch 'diff-eq-subs-attempt'

kangwonlee · Jun 23, 2024 · 43d0362 · 43d0362
2 parents 3ed13e2 + b66c77c
commit 43d0362
Showing 1 changed file with 148 additions and 7 deletions.
diff --git a/35_sympy/10_sympy.ipynb b/35_sympy/10_sympy.ipynb
@@ -1811,7 +1811,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 미분방정식<br>Differential Equations\n",
+    "## Differential Equations<br>미분방정식\n",
     "\n"
    ]
   },
@@ -1830,6 +1830,9 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "import sympy as sym\n",
+    "\n",
+    "\n",
     "f = sym.Function('f', real=True)\n",
     "\n"
    ]
@@ -1869,7 +1872,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Free Vibration of a Mechanical System<br>기계시스템의 자유진동\n",
+    "### Free Vibration of a Mechanical System<br>기계시스템의 자유진동\n",
     "\n"
    ]
   },
@@ -1912,7 +1915,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Initial conditions<br>초기조건\n",
+    "#### **Initial** conditions<br>초기조건\n",
     "\n"
    ]
   },
@@ -2002,7 +2005,145 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Forced Vibration<br>강제진동\n",
+    "#### Substitution approach<br>대입법\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "A, B, zeta, omega, phi = sym.symbols('A B zeta omega phi', real=True)\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "f = sym.exp(zeta * t) * (A * sym.sin(omega * t) + B * sym.cos(omega * t))\n",
+    "f\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df = f.diff(t)\n",
+    "df\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df2 = df.diff(t)\n",
+    "df2\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "diff_eq = sym.simplify(sym.Eq(m * df2 + c * df + k * f, 0))\n",
+    "diff_eq\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "collected = sym.collect(sym.expand(diff_eq.lhs), [sym.exp(t*zeta)*sym.sin(omega * t), sym.exp(t*zeta)*sym.cos(omega * t)])\n",
+    "collected\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cos_term = collected.args[1]\n",
+    "sin_term = collected.args[0]\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq00 = sym.Eq(cos_term / (sym.exp(t*zeta)*sym.cos(omega * t)), 0)\n",
+    "eq00\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq01 = sym.Eq(sin_term / (sym.exp(t*zeta)*sym.sin(omega * t)), 0)\n",
+    "eq01\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq1 = sym.Eq(f.subs({t:0}), x0)\n",
+    "eq1\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "eq2 = sym.Eq(df.subs({t:0}), v0)\n",
+    "eq2\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "sym.solve([eq00, eq01, eq1, eq2], [A, B, zeta, omega])\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Forced Vibration<br>강제진동\n",
     "\n"
    ]
   },
@@ -2091,8 +2232,8 @@
  ],
  "metadata": {
   "colab": {
-   "include_colab_link": true,
-   "provenance": []
+   "provenance": [],
+   "include_colab_link": true
   },
   "kernelspec": {
    "display_name": "Python 3 (ipykernel)",
@@ -2113,5 +2254,5 @@
   }
  },
  "nbformat": 4,
- "nbformat_minor": 4
+ "nbformat_minor": 0
 }