Multibody dynamics
Graduate · Engineering
Syllabus focus
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
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Kinematics and constraints
Multibody system topology and graphs
Coming soon - Dynamics formulations
Newton-Euler equations for bodies
Coming soon - Software and vehicle dynamics
ADAMS, Simscape Multibody, or RecurDyn labs
Coming soon - Research applications
Biomechanics multibody models of gait
Coming soon
Notes
Topics reflect common engineering syllabi at US colleges and universities. Exact order, depth, and applied emphasis vary by institution, department, and instructor.