Physics MCP Server

Steps the simulation and records position/orientation/velocity at each
timestep for one body. Perfect for generating animation data for R3F.

Args:
    sim_id: Simulation ID
    body_id: ID of the body to track
    steps: Number of timesteps to record
    dt: Optional timestep override. If None, uses config default.

Returns:
    TrajectoryResponse containing:
        - body_id: Tracked body identifier
        - frames: List of trajectory frames with time, position, orientation, velocity
        - total_time: Total simulated time in seconds
        - num_frames: Number of frames recorded

Tips for LLMs:
    - Each frame has: time, position [x,y,z], orientation [x,y,z,w], velocity [x,y,z]
    - Frames are evenly spaced in time (every dt seconds)
    - Output is R3F-compatible: use position/orientation directly in Three.js
    - For 60 FPS video: record at dt=1/60 ≈ 0.0167
    - Typical recording: 100-1000 frames (1.6-16 seconds at 60 FPS)

Example:
    # Record 5 seconds of a falling ball
    traj = await record_trajectory(
        sim_id=sim_id,
        body_id="ball",
        steps=300  # 300 × 0.016 ≈ 5 seconds
    )
    # Use traj.frames in React Three Fiber for animation