Progress towards firmware

docs/motion-control.ipynb

@@ -318,6 +318,32 @@
     "p3 = p1s7[\"pe\"].subs({t_a: 0, t_v: 0}).simplify()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 36,
+   "id": "06638377-bd46-4b62-84d5-05271c6ef7ab",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle - \\frac{a_{max}}{j_{max}} + \\frac{v_{max}}{a_{max}}$"
+      ],
+      "text/plain": [
+       "  aₘₐₓ   vₘₐₓ\n",
+       "- ──── + ────\n",
+       "  jₘₐₓ   aₘₐₓ"
+      ]
+     },
+     "execution_count": 36,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "t_a_max"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 16,
@@ -347,7 +373,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 38,
    "id": "5f779934-7f89-4ef4-9f89-d268a9742059",
    "metadata": {},
    "outputs": [
@@ -365,43 +391,69 @@
        "               2⋅╲╱ aₘₐₓ ⋅jₘₐₓ           "
       ]
      },
-     "execution_count": 17,
+     "execution_count": 38,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "p2ta = sympy.solve(p - p2, t_a, positive=True)[0]\n",
+    "p2ta = sympy.solve(p - p2, t_a, positive=True)[0].simplify()\n",
     "sympy.Eq(t_a, p2ta)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 55,
+   "id": "a0a4fc4f-e5a5-4c91-b8be-cc80f710438f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{a_{max}^{3} + 4 j_{max}^{2} p}{4 a_{max} j_{max}^{2}}$"
+      ],
+      "text/plain": [
+       "    3         2  \n",
+       "aₘₐₓ  + 4⋅jₘₐₓ ⋅p\n",
+       "─────────────────\n",
+       "              2  \n",
+       "   4⋅aₘₐₓ⋅jₘₐₓ   "
+      ]
+     },
+     "execution_count": 55,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(p2ta + 3*(a_max ** sympy.Rational(3,2)) / (2 * a_max ** sympy.Rational(1,2) * j_max)).simplify() ** 2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 35,
    "id": "5e61c9d2-09f5-4585-999a-e9c786451520",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/latex": [
-       "$\\displaystyle t_{j} = \\frac{2^{\\frac{2}{3}} \\sqrt[3]{p}}{2 \\sqrt[3]{j_{max}}}$"
+       "$\\displaystyle t_{j} = \\frac{p}{2 j_{max}}$"
       ],
       "text/plain": [
-       "       2/3 3 ___\n",
-       "      2   ⋅╲╱ p \n",
-       "t_j = ──────────\n",
-       "        3 ______\n",
-       "      2⋅╲╱ jₘₐₓ "
+       "        p   \n",
+       "t_j = ──────\n",
+       "      2⋅jₘₐₓ"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "p3tj = sympy.solve(p - p3, t_j)[0]\n",
-    "sympy.Eq(t_j, p3tj)"
+    "sympy.Eq(t_j, (p3tj**3))"
    ]
   },
   {
@@ -626,9 +678,36 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 61,
    "id": "dbacdbe8-1ced-4bf5-872e-e68a1b9ff7db",
    "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{j_{max} t_{j} \\left(t_{a}^{2} + 3 t_{a} t_{j} + 2 t_{j}^{2}\\right)}{2}$"
+      ],
+      "text/plain": [
+       "         ⎛  2                   2⎞\n",
+       "jₘₐₓ⋅t_j⋅⎝tₐ  + 3⋅tₐ⋅t_j + 2⋅t_j ⎠\n",
+       "──────────────────────────────────\n",
+       "                2                 "
+      ]
+     },
+     "execution_count": 61,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "p1s3[\"pe\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a63210fc-0c10-43ad-b78e-ec3b0814b8e1",
+   "metadata": {},
    "outputs": [],
    "source": []
   }