01 | Module
Introduction to Multibody Systems and Simulation
Bodies, joints, and forces, tree and closed-loop topology, and the degree-of-freedom count.
Start module →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.
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- Used in Career directions
- Content status
- Lesson hub
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
01
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.
Grounded in Wittenburg
The course follows Wittenburg, Dynamics of Multibody Systems, from rigid-body kinematics through the general equations of motion to impacts, so the vocabulary matches the formalism used in real multibody software.
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.
02
The 10 modules
02 | Module
Rigid-Body Kinematics: Position and Orientation
Rotation matrices, Euler and Bryan angles, angular velocity, and Euler parameters.
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Generalized Coordinates and Degrees of Freedom
Minimal coordinates and the Grubler-Kutzbach mobility criterion in the plane and in space.
Start module →04 | Module
Kinematic Constraints and Joints
Holonomic and nonholonomic constraints, the Jacobian, and velocity and acceleration analysis.
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Mass, Inertia, and Momentum
The inertia tensor, the parallel-axis theorem, kinetic energy, and angular momentum.
Start module →06 | Module
Newton-Euler Equations of Motion
Force to acceleration for the mass center and Euler’s equations for three-dimensional spin.
Start module →07 | Module
Lagrangian Dynamics and Virtual Work
Energy methods, generalized forces by virtual work, and Lagrange multipliers.
Start module →08 | Module
Constrained Equations of Motion (DAEs)
The augmented system, multipliers as reactions, differential index, and Baumgarte stabilization.
Start module →09 | Module
Numerical Simulation of Multibody Systems
State-space form, explicit and implicit integrators, DAE solvers, and choosing a time step.
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Impacts, Contact, and Simulation Validation
Impulsive dynamics and restitution, and validating a model by momentum, energy, and constraints.
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