Course 23 | Advanced Engineering Methods
Multibody Dynamics and Mechanical-System Simulation
Model connected rigid bodies with joints and forces, then build and integrate their equations of motion into checked mechanical-system simulations.
Course snapshot
- Purpose
- Multibody dynamics teaches how to turn a mechanism, vehicle, or robot into constrained equations of motion and simulate its motion over time.
- Prerequisites
- Related advanced methods
- Used in Career Directions
Choose later
How to study this course
- Define bodies, joints, and forces
- Choose generalized coordinates
- Write the constraint equations
- Assemble the equations of motion
- Integrate the motion in time
- Check energy, constraints, and a hand estimate
How this course is designed
Model before you solve
Every study starts by naming the bodies, joints, and forces and counting the degrees of freedom. That count sizes the problem and tells you how many inputs and initial conditions a simulation needs, before a single equation is written.
Every result is checkable
Each module ends in a quantity: a degree-of-freedom count, a constraint Jacobian, a Lagrange multiplier, a stable time step, or a conserved energy, the evidence that turns a running simulation into a defensible result.
The 10 modules
01 | Module
Introduction to Multibody Systems and Simulation
Bodies, joints, and forces, tree and closed-loop topology, and the degree-of-freedom count.
02 | Module
Rigid-Body Kinematics: Position and Orientation
Rotation matrices, Euler and Bryan angles, angular velocity, and Euler parameters.
03 | Module
Generalized Coordinates and Degrees of Freedom
Minimal coordinates and the Grubler-Kutzbach mobility criterion in the plane and in space.
04 | Module
Kinematic Constraints and Joints
Holonomic and nonholonomic constraints, the Jacobian, and velocity and acceleration analysis.
05 | Module
Mass, Inertia, and Momentum
The inertia tensor, the parallel-axis theorem, kinetic energy, and angular momentum.
06 | Module
Newton-Euler Equations of Motion
Force to acceleration for the mass center and Euler’s equations for three-dimensional spin.
07 | Module
Lagrangian Dynamics and Virtual Work
Energy methods, generalized forces by virtual work, and Lagrange multipliers.
08 | Module
Constrained Equations of Motion (DAEs)
The augmented system, multipliers as reactions, differential index, and Baumgarte stabilization.
09 | Module
Numerical Simulation of Multibody Systems
State-space form, explicit and implicit integrators, DAE solvers, and choosing a time step.
10 | Module
Impacts, Contact, and Simulation Validation
Impulsive dynamics and restitution, and validating a model by momentum, energy, and constraints.