Multibody dynamics
Graduate · Engineering
Syllabus focus
Standard syllabus · STEM / applied
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Standard syllabus
Kinematics and constraints
- Multibody system topology and graphs
- Absolute and relative coordinates
- Holonomic and nonholonomic constraints
- Constraint equations and Jacobian matrices
- Index-3 DAE structure in multibody models
- Redundant constraint detection and stabilization
- Kinematic loops and closed-chain mechanisms
- Joint types: revolute, prismatic, spherical, universal
- Driver constraints and prescribed motion
- Singular configurations and redundancy resolution
Dynamics formulations
- Newton-Euler equations for bodies
- Lagrange multipliers for constrained dynamics
- Kane's method and Jourdain's principle (survey)
- Mass matrix assembly for multibody systems
- Coriolis and centrifugal force terms
- Energy and momentum conservation checks
- Impact and contact models: penalty and restitution
- Flexible multibody: floating frame of reference
- Modal reduction for flexible bodies
- Numerical integration of stiff multibody DAEs
STEM / applied
Software and vehicle dynamics
- ADAMS, Simscape Multibody, or RecurDyn labs
- Automotive suspension and steering models
- Railway vehicle dynamics and hunting
- Robotic manipulator multibody simulation
- Track geometry and road profile inputs
- Parameter identification from test data
- Co-simulation with controls and hydraulics
- Real-time multibody for hardware-in-the-loop
- Thesis project using multibody software
- Validation against benchmark mechanisms
Research applications
- Biomechanics multibody models of gait
- Wind turbine drivetrain dynamics
- Gear and chain contact force prediction
- Cable-driven parallel robots
- Spacecraft deployment multibody simulation
- Machine learning for multibody surrogate models
- Parallel computing for large multibody systems
- Journal club on multibody dynamics papers
- Industry collaboration on vehicle NVH
- Qualifying exam multibody preparation
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.