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Mathematical Model → Physics Simulation
June 8, 2025
Once your CAD model has been converted into USD and organized into a simulation-ready stage, the next step is defining the mathematical rules that govern its behavior. In Omniverse, this means attaching physics properties to your objects and configuring the PhysX engine to simulate motion, collisions, forces, and constraints. This post walks through how the simulation engine acts as your mathematical model—and how to configure it for both deterministic and stochastic use cases.
What Is the Mathematical Model?
In classical simulation modeling, a mathematical model refers to a system of equations (often differential equations) that describe how a system evolves over time. In Omniverse, you don’t have to write those equations by hand. Instead, Omniverse’s PhysX engine interprets mass, velocity, joint constraints, and external forces to simulate those dynamics for you—frame by frame.
Continuous Physics in Omniverse
Omniverse simulates continuous motion using a time-stepped solver. At each simulation tick (e.g., 60 or 120 Hz), the engine performs the following:
- Reads State
- Gathers positions, velocities, and forces from each rigid body or articulated joint.
- Solves Dynamics
- Computes the effects of gravity, joint limits, contacts, and collisions using the PhysX solver.
- Updates State
- Applies the computed forces and writes back the updated state into the USD scene.
This continuous loop forms the “engine” of your simulation. It runs as long as the simulation is active—whether in real time (interactive mode) or headless batch mode.
How to Configure the Mathematical Model
To get accurate and meaningful results from simulation, you need to configure the right physical parameters on your USD prims.
1. Rigid Body Setup
- Apply the
physxRigidBodyAPIto any object you want to simulate dynamically. - Key attributes:
mass: total mass of the body.linearDamping,angularDamping: to simulate air resistance or internal friction.startVelocity: for initial movement.disableGravity: if you want the object to float.
2. Joints and Constraints
- Use
physxJointAPI(revolute, prismatic, spherical, etc.) to connect bodies. - Configure limits like max angle, spring stiffness, damping, and break thresholds.
3. Collision Properties
- Apply
collisionAPIwith:collisionEnabled = truecollisionGeometry: convex hull or meshrestitution,friction: for bounces and sliding behavior
4. Gravity and Global Physics Settings
- Scene-wide settings include:
gravityDirection = (0, -1, 0)gravityMagnitude = 9.81solverIterations = 8–32depending on stiffness of constraints
Deterministic vs. Stochastic ⚖️
- Deterministic:
- Fixed seed, no random logic = same result every run.
- Ideal for debugging and validation.
- Stochastic:
- Inject randomness via Python (e.g., wind, delays).
- Run multiple seeds for statistical confidence.
// Pseudocode: random force once per second
if time_changed_by_1_sec:
force = random(-3, 3)
applyForce("WingLeft", force)
Common Pitfalls
- No motion → gravity off or object is static.
- Instability → mass too low or solver iterations too few.
- Drift → bad collision shapes or incorrect inertia.
- Always verify with deterministic runs first.
- Use Omniverse’s physics visualizer for force/joint debugging.
- Match materials and densities to real-world references.
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