Physics MCP Server

Creates a new physics body (static, dynamic, or kinematic) with specified
shape, mass, and initial conditions. Bodies interact via collisions.

Args:
    sim_id: Simulation ID from create_simulation
    body_id: Unique identifier for this body (user-defined string)
    body_type: "static", "dynamic", or "kinematic"
        - static: Never moves (ground, walls)
        - dynamic: Affected by forces and collisions
        - kinematic: Moves but not affected by forces (scripted motion)
    shape: Collider shape: "box", "sphere", "capsule", "cylinder", "plane"
    size: Shape dimensions:
        - box: [width, height, depth]
        - sphere: [radius]
        - capsule: [half_height, radius]
        - cylinder: [half_height, radius]
        - plane: not needed (use normal/offset instead)
    mass: Mass in kilograms (for dynamic bodies). Default 1.0
    normal: Normal vector [x, y, z] for plane shape. Default [0, 1, 0] (upward)
    offset: Offset along normal for plane. Default 0.0
    position: Initial position [x, y, z]. Default [0, 0, 0]
    orientation: Initial orientation quaternion [x, y, z, w]. Default [0, 0, 0, 1] (identity)
    velocity: Initial linear velocity [x, y, z]. Default [0, 0, 0]
    angular_velocity: Initial angular velocity [x, y, z]. Default [0, 0, 0]
    restitution: Bounciness (0.0 = no bounce, 1.0 = perfect bounce). Default 0.5
    friction: Surface friction (0.0 = ice, 1.0 = rubber). Default 0.5
    is_sensor: If true, detects collisions but doesn't respond physically. Default false
    linear_damping: Linear velocity damping (0.0-1.0) - like air resistance. Default 0.0
    angular_damping: Angular velocity damping (0.0-1.0) - like rotational friction. Default 0.0
    drag_coefficient: Base drag coefficient (Cd) for orientation-dependent drag. Optional
    drag_area: Reference cross-sectional area (m²) for drag calculation. Optional
    drag_axis_ratios: Drag variation along body axes [x, y, z]. E.g., [1.0, 0.2, 1.0] for streamlined along Y. Optional
    fluid_density: Fluid density (kg/m³). Air=1.225, Water=1000. Default 1.225

Returns:
    body_id (echo of the input ID)

Tips for LLMs:
    - Create ground FIRST: body_type="static", shape="plane", normal=[0, 1, 0]
    - Box size is full width/height/depth (not half-extents)
    - Sphere size is [radius] (array with one element)
    - Quaternions: identity = [0, 0, 0, 1] (no rotation)
    - Common restitution: steel=0.8, wood=0.5, clay=0.1
    - Common friction: ice=0.05, wood=0.4, rubber=1.0

Example:
    # Add a ground plane
    await add_rigid_body(
        sim_id=sim_id,
        body_id="ground",
        body_type="static",
        shape="plane",
        normal=[0, 1, 0]
    )

    # Add a bouncing ball
    await add_rigid_body(
        sim_id=sim_id,
        body_id="ball",
        body_type="dynamic",
        shape="sphere",
        size=[0.5],  # radius = 0.5m
        mass=1.0,
        position=[0, 10, 0],
        restitution=0.7
    )

    # Add a falling box
    await add_rigid_body(
        sim_id=sim_id,
        body_id="box",
        body_type="dynamic",
        shape="box",
        size=[1.0, 1.0, 1.0],
        mass=10.0,
        position=[0.0, 5.0, 0.0]
    )