Merge pull request #149 from chvmvd/change-variable-name-#124

Change v_x => u v_y => v #124

Author: chvmvd

docs/02advanced/03simulation/02parabolic_motion/index.mdx

@@ -11,37 +11,37 @@ import Answer from "@site/src/components/Answer";
 
 次は、もう少し複雑な放物運動を考えましょう。
 
-初速度を $v_0$ 、$x$ 軸方向の速度を $v_x$ 、$y$ 軸方向の速度を $v_y$ 、重力加速度を $g$ 、 $t$ 秒後の変位を $x,y$ として、仰角 $\theta$ で物体を投げたとします。
+初速度を $v_0$ 、$x$ 軸方向の速度を $u$ 、$y$ 軸方向の速度を $v$ 、重力加速度を $g$ 、 $t$ 秒後の変位を $x,y$ として、仰角 $\theta$ で物体を投げたとします。
 
 これらの関係は、次のようになります。
 
 $$
 \begin{align*}
-    \frac{dx}{dt}   &= v_x \\
-    \frac{dy}{dt}   &= v_y \\
-    \frac{dv_x}{dt} &= 0 \\
-    \frac{dv_y}{dt} &= -g
+    \frac{dx}{dt}   &= u \\
+    \frac{dy}{dt}   &= v \\
+    \frac{du}{dt} &= 0 \\
+    \frac{dv}{dt} &= -g
 \end{align*}
 $$
 
 これを差分化してみましょう。
 
 $$
 \begin{align*}
-    \frac{x_{n + 1} - x_n}{\Delta t}              &= {v_x}_n \\
-    \therefore x_{n + 1} - x_n                    &= {v_x}_n \Delta t \\
-    \therefore x_{n + 1}                          &= x_n + {v_x}_n \Delta t
+    \frac{x_{n + 1} - x_n}{\Delta t}              &= u_n \\
+    \therefore x_{n + 1} - x_n                    &= u_n \Delta t \\
+    \therefore x_{n + 1}                          &= x_n + u_n \Delta t
 \end{align*}
 $$
 
 他も同様にすると、次のようになります。
 
 $$
 \begin{align*}
-    x_{n + 1}     &= x_n + {v_x}_n \Delta t \\
-    y_{n + 1}     &= y_n + {v_y}_n \Delta t \\
-    {v_x}_{n + 1} &= {v_x}_n \\
-    {v_y}_{n + 1} &= {v_y}_n - g\Delta t
+    x_{n + 1}     &= x_n + u_n \Delta t \\
+    y_{n + 1}     &= y_n + v_n \Delta t \\
+    u_{n + 1} &= u_n \\
+    v_{n + 1} &= v_n - g\Delta t
 \end{align*}
 $$
 

static/simulation/parabolic_motion.ipynb

@@ -1,55 +1,55 @@
 {
- "nbformat": 4,
- "nbformat_minor": 2,
- "metadata": {},
- "cells": [
-  {
-   "metadata": {},
-   "source": [
-    "import math"
-   ],
-   "cell_type": "code",
-   "outputs": [],
-   "execution_count": null
-  },
-  {
-   "metadata": {},
-   "source": [
-    "g = 9.8\n",
-    "\n",
-    "\n",
-    "def parabolic_motion_step(x, y, vx, vy, dt):\n",
-    "    x = x + vx * dt\n",
-    "    y = y + vy * dt\n",
-    "    vx = vx\n",
-    "    vy = vy - g * dt\n",
-    "    return [x, y, vx, vy]\n",
-    "\n",
-    "\n",
-    "def parabolic_motion(v0, theta, t, dt):\n",
-    "    x = 0\n",
-    "    y = 0\n",
-    "    vx = v0 * math.cos(theta)\n",
-    "    vy = v0 * math.sin(theta)\n",
-    "    n = int(t / dt)\n",
-    "    for i in range(n):\n",
-    "        x, y, vx, vy = parabolic_motion_step(x, y, vx, vy, dt)\n",
-    "    return [x, y]\n",
-    "\n",
-    "\n",
-    "print(parabolic_motion(30, math.pi / 4, 4, 0.01))"
-   ],
-   "cell_type": "code",
-   "outputs": [
+  "nbformat": 4,
+  "nbformat_minor": 2,
+  "metadata": {},
+  "cells": [
     {
-     "output_type": "stream",
-     "name": "stdout",
-     "text": [
-      "[84.85281374238573, 6.648813742385697]\n"
-     ]
+      "metadata": {},
+      "source": [
+        "import math"
+      ],
+      "cell_type": "code",
+      "outputs": [],
+      "execution_count": null
+    },
+    {
+      "metadata": {},
+      "source": [
+        "g = 9.8\n",
+        "\n",
+        "\n",
+        "def parabolic_motion_step(x, y, u, v, dt):\n",
+        "    x = x + u * dt\n",
+        "    y = y + v * dt\n",
+        "    u = u\n",
+        "    v = v - g * dt\n",
+        "    return [x, y, u, v]\n",
+        "\n",
+        "\n",
+        "def parabolic_motion(v0, theta, t, dt):\n",
+        "    x = 0\n",
+        "    y = 0\n",
+        "    u = v0 * math.cos(theta)\n",
+        "    v = v0 * math.sin(theta)\n",
+        "    n = int(t / dt)\n",
+        "    for i in range(n):\n",
+        "        x, y, u, v = parabolic_motion_step(x, y, u, v, dt)\n",
+        "    return [x, y]\n",
+        "\n",
+        "\n",
+        "print(parabolic_motion(30, math.pi / 4, 4, 0.01))"
+      ],
+      "cell_type": "code",
+      "outputs": [
+        {
+          "output_type": "stream",
+          "name": "stdout",
+          "text": [
+            "[84.85281374238573, 6.648813742385697]\n"
+          ]
+        }
+      ],
+      "execution_count": null
     }
-   ],
-   "execution_count": null
-  }
- ]
+  ]
 }