Differential_Algebraic_Equations.ipynb

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                  "text/plain": "<Figure size 600x600 with 1 Axes>",
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        "<a href=\"https://colab.research.google.com/github/walkerjian/Physics/blob/main/Differential_Algebraic_Equations.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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        "# **Introduction to Differential-Algebraic Equations (DAEs)**\n",
        "\n",
        "**Differential-algebraic equations (DAEs)** are systems of equations that consist of both differential and algebraic components. They generalize ordinary differential equations (ODEs) by allowing constraints that do not involve derivatives, resulting in a more complex interplay between dynamics and constraints.\n",
        "\n",
        "DAEs arise naturally in many areas, such as control systems, electrical circuit simulation, robotics, chemical engineering, and fluid dynamics. Unlike ODEs, DAEs often include implicit relationships between variables, making their analysis and numerical solution more challenging.\n",
        "\n",
        "## 1. **What Are DAEs?**\n",
        "\n",
        "A DAE can be written in the general form:\n",
        "\n",
        "$$\n",
        "F(t, y(t), \\dot{y}(t)) = 0,\n",
        "$$\n",
        "\n",
        "where:\n",
        "- $ y(t) $ is the state vector (dependent variables),\n",
        "- $ \\dot{y}(t) $ represents the time derivatives of $ y(t) $,\n",
        "- $ t $ is the independent variable (usually time),\n",
        "- $ F $ is a function representing the system dynamics and constraints.\n",
        "\n",
        "The key distinction between DAEs and ODEs is the presence of algebraic constraints, which often involve $ y(t) $ but not $ \\dot{y}(t) $.\n",
        "\n",
        "---\n",
        "\n",
        "## 2. **Index of a DAE**\n",
        "\n",
        "The **index** of a DAE measures its \"difficulty\" by quantifying the number of times algebraic constraints must be differentiated to reduce the system to an equivalent ODE form. Common types include:\n",
        "- **Index-1 DAEs**: Constraints can be resolved directly for the algebraic variables.\n",
        "- **Index-2 and higher DAEs**: Require differentiation of constraints to reduce them to an index-1 or ODE form.\n",
        "\n",
        "For example:\n",
        "- Consider the pendulum equations in Cartesian coordinates:\n",
        "  $$\n",
        "  \\dot{x} = v_x, \\quad \\dot{y} = v_y, \\quad m \\dot{v}_x = -\\lambda x, \\quad m \\dot{v}_y = -mg - \\lambda y,\n",
        "  $$\n",
        "  with the algebraic constraint:\n",
        "  $$\n",
        "  x^2 + y^2 - l^2 = 0.\n",
        "  $$\n",
        "\n",
        "---\n",
        "\n",
        "## 3. **Applications of DAEs**\n",
        "\n",
        "1. **Electrical Circuits**: DAEs naturally describe circuits via Kirchhoff's laws, combining dynamic components (capacitors and inductors) with algebraic constraints (voltage and current relationships).\n",
        "   \n",
        "2. **Mechanical Systems**: Multibody systems with constraints (e.g., robotic arms or pendulums) are modeled as DAEs.\n",
        "\n",
        "3. **Chemical Engineering**: Reaction kinetics combined with conservation laws often lead to DAEs.\n",
        "\n",
        "4. **Optimal Control**: Problems where control variables are constrained often result in DAEs.\n",
        "\n",
        "---\n",
        "\n",
        "## 4. **Numerical Methods for Solving DAEs**\n",
        "\n",
        "Numerical solution of DAEs is more involved than solving ODEs. Popular approaches include:\n",
        "\n",
        "1. **Reduction to ODEs**: For index-1 systems, algebraic constraints are solved explicitly (if possible).\n",
        "\n",
        "2. **Implicit Methods**: Methods such as the backward differentiation formula (BDF) are widely used for stiff DAEs.\n",
        "\n",
        "3. **Differentiation-Based Methods**: Higher-index DAEs often require differentiating constraints to reduce the index.\n",
        "\n",
        "4. **Stabilization Techniques**: For index-2 or higher, stabilization methods like projection or penalty techniques may be used.\n",
        "\n",
        "---\n",
        "\n",
        "## 5. **Exercises and Examples**\n",
        "\n",
        "### Example 1: Solving an Index-1 DAE\n",
        "\n",
        "Consider the system:\n",
        "$$\n",
        "\\begin{aligned}\n",
        "\\dot{x} &= -y, \\\\\n",
        "x^2 + y^2 &= 1.\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "Here, the algebraic constraint $ x^2 + y^2 = 1 $ defines a unit circle.\n",
        "\n",
        "- **Task**: Solve this system numerically using Python.\n",
        "- **Steps**:\n",
        "  1. Reformulate the system using Lagrange multipliers or implicit solvers.\n",
        "  2. Use `scipy.integrate.solve_ivp` with the Radau method for stiff systems.\n",
        "---\n"
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import solve_ivp\n",
        "\n",
        "# Define the DAE system\n",
        "def dae_system(t, z):\n",
        "    x, y, lambda_ = z\n",
        "    dxdt = -y\n",
        "    dydt = x\n",
        "    constraint = x**2 + y**2 - 1\n",
        "    return [dxdt, dydt, constraint]\n",
        "\n",
        "# Initial conditions\n",
        "z0 = [1.0, 0.0, 0.0]  # x, y, lambda\n",
        "t_span = (0, 10)\n",
        "t_eval = np.linspace(*t_span, 100)\n",
        "\n",
        "# Solve the system\n",
        "solution = solve_ivp(dae_system, t_span, z0, method='Radau', t_eval=t_eval)\n",
        "\n",
        "# Plot the solution\n",
        "import matplotlib.pyplot as plt\n",
        "plt.plot(solution.y[0], solution.y[1])\n",
        "plt.xlabel(\"x\")\n",
        "plt.ylabel(\"y\")\n",
        "plt.title(\"Trajectory on the Unit Circle\")\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "\n",
        "### Example 2: A Simple Electrical Circuit\n",
        "\n",
        "Simulate an RLC circuit described by the DAE:\n",
        "$$\n",
        "\\begin{aligned}\n",
        "V - RI - L\\dot{I} - Q/C &= 0, \\\\\n",
        "\\dot{Q} - I &= 0.\n",
        "\\end{aligned}\n",
        "$$\n",
        "\n",
        "- **Task**: Solve numerically with given initial conditions.\n",
        "- **Steps**: Implement the equations in Python, solving with `solve_ivp`.\n",
        "\n",
        "---"
      ],
      "metadata": {
        "id": "67CD5pnw8Mvz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import solve_ivp\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Parameters for the RLC circuit\n",
        "R = 10  # Resistance (Ohms)\n",
        "L = 0.1  # Inductance (Henries)\n",
        "C = 0.001  # Capacitance (Farads)\n",
        "V = 5  # Voltage source (Volts)\n",
        "\n",
        "# Define the DAE system\n",
        "def rlc_dae(t, z):\n",
        "    Q, I = z  # Q: charge on the capacitor, I: current through the circuit\n",
        "    dQdt = I\n",
        "    dIdt = (V - R * I - Q / C) / L  # Derived from Kirchhoff's voltage law\n",
        "    return [dQdt, dIdt]\n",
        "\n",
        "# Initial conditions\n",
        "Q0 = 0  # Initial charge on the capacitor\n",
        "I0 = 0  # Initial current\n",
        "z0 = [Q0, I0]\n",
        "\n",
        "# Time span for the simulation\n",
        "t_span = (0, 0.01)  # Simulate for 10 milliseconds\n",
        "t_eval = np.linspace(*t_span, 1000)  # 1000 time points for smooth plotting\n",
        "\n",
        "# Solve the DAE system\n",
        "solution = solve_ivp(rlc_dae, t_span, z0, method='Radau', t_eval=t_eval)\n",
        "\n",
        "# Extract results\n",
        "Q = solution.y[0]  # Charge on the capacitor\n",
        "I = solution.y[1]  # Current in the circuit\n",
        "\n",
        "# Calculate the voltage across the capacitor\n",
        "V_cap = Q / C\n",
        "\n",
        "# Plot the results\n",
        "plt.figure(figsize=(10, 6))\n",
        "\n",
        "# Plot current\n",
        "plt.subplot(3, 1, 1)\n",
        "plt.plot(solution.t, I, label='Current (I)', color='blue')\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Current (A)')\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "\n",
        "# Plot charge\n",
        "plt.subplot(3, 1, 2)\n",
        "plt.plot(solution.t, Q, label='Charge (Q)', color='orange')\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Charge (C)')\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "\n",
        "# Plot capacitor voltage\n",
        "plt.subplot(3, 1, 3)\n",
        "plt.plot(solution.t, V_cap, label='Voltage (V_cap)', color='green')\n",
        "plt.xlabel('Time (s)')\n",
        "plt.ylabel('Voltage (V)')\n",
        "plt.grid()\n",
        "plt.legend()\n",
        "\n",
        "plt.tight_layout()\n",
        "plt.show()\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "id": "zHB2EO2i8Vz9",
        "outputId": "0e287582-27c0-42bc-daa8-77623c8f878b"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 3 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Example 3: Pendulum System in Cartesian Coordinates\n",
        "\n",
        "- Solve the pendulum equations numerically and visualize the motion in Cartesian coordinates. Add damping for a realistic scenario.\n",
        "**WIP**\n",
        "---"
      ],
      "metadata": {
        "id": "IVpDq5lY8RKX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from scipy.integrate import solve_ivp\n",
        "import matplotlib.pyplot as plt\n",
        "from ipywidgets import interact, FloatSlider\n",
        "\n",
        "# Parameters for the pendulum\n",
        "l = 1.0  # Length of the pendulum (m)\n",
        "m = 1.0  # Mass of the pendulum (kg)\n",
        "g = 9.81  # Gravitational acceleration (m/s^2)\n",
        "\n",
        "# Define the DAE system for the pendulum\n",
        "def pendulum_dae(t, z):\n",
        "    x, y, vx, vy, lambda_ = z\n",
        "\n",
        "    dxdt = vx\n",
        "    dydt = vy\n",
        "    dvxdt = -lambda_ * x / m\n",
        "    dvydt = -g - lambda_ * y / m\n",
        "    constraint = x**2 + y**2 - l**2\n",
        "\n",
        "    return [dxdt, dydt, dvxdt, dvydt, constraint]\n",
        "\n",
        "# Initial conditions\n",
        "x0, y0 = 1.0, 0.0  # Start at the end of the pendulum\n",
        "vx0, vy0 = 0.0, 0.0  # No initial velocity\n",
        "lambda0 = 0.0  # Initial Lagrange multiplier\n",
        "z0 = [x0, y0, vx0, vy0, lambda0]\n",
        "\n",
        "# Time span for the simulation\n",
        "t_span = (0, 10)\n",
        "t_eval = np.linspace(*t_span, 500)\n",
        "\n",
        "# Solve the DAE system\n",
        "def solve_pendulum(length, gravity):\n",
        "    global l, g\n",
        "    l = length\n",
        "    g = gravity\n",
        "    solution = solve_ivp(pendulum_dae, t_span, z0, method='Radau', t_eval=t_eval)\n",
        "    x = solution.y[0]\n",
        "    y = solution.y[1]\n",
        "    return x, y, solution.t\n",
        "\n",
        "# Interactive plot with sliders\n",
        "def plot_pendulum(length=1.0, gravity=9.81):\n",
        "    x, y, t = solve_pendulum(length, gravity)\n",
        "\n",
        "    plt.figure(figsize=(6, 6))\n",
        "    plt.plot(x, y, label=\"Pendulum Trajectory\")\n",
        "    plt.scatter([0], [0], color='red', label=\"Pivot Point\")\n",
        "    plt.xlabel(\"x (m)\")\n",
        "    plt.ylabel(\"y (m)\")\n",
        "    plt.title(f\"Pendulum Trajectory (Length={length}m, Gravity={gravity}m/s^2)\")\n",
        "    plt.grid()\n",
        "    plt.legend()\n",
        "    plt.axis('equal')\n",
        "    plt.show()\n",
        "\n",
        "# Create sliders to control parameters\n",
        "interact(plot_pendulum,\n",
        "         length=FloatSlider(value=1.0, min=0.5, max=2.0, step=0.1, description=\"Length (m)\"),\n",
        "         gravity=FloatSlider(value=9.81, min=1.0, max=20.0, step=0.5, description=\"Gravity (m/s^2)\"));\n"
      ],
      "metadata": {
        "colab": {
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      "cell_type": "markdown",
      "source": [
        "## Next Steps\n",
        "\n",
        "To explore DAEs further:\n",
        "- Study specific numerical methods like **Gear's method** or **collocation methods**.\n",
        "- Implement DAEs in Mathematica using `NDSolve` with constraints.\n",
        "- Explore index-reduction techniques and their applications.\n",
        "\n",
        "This framework should provide a strong foundation for further study, reinforced by hands-on computational exercises!"
      ],
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}