Unit 1 Basic concepts in 3-D rigid-body mechanics

11 lecture hours

• Rigid body vs flexible body
• Spatial kinematics (3-D rotation transformations)
• Euler theorem
• rotation Program Name: Master of Engineering Level: PG Branch: Machine Design Subject Code : ME02078031 Subject Name : Multibody Dynamics parameterization
• Rodriguez formula
• Moments and products of inertia
• Newton-Euler equations of motion
• Lagrange Equation
• Generalized forces

Unit 2 Inter-connected rigid bodies

6 lecture hours

• Kinematic pairs (joints) with classification of constraints
• holonomic and non-holonomic constraints
• actuators and controllers with brief introduction of controls theory

Unit 3 Formulation of equations of motion for inter-connected bodies

12 lecture hours

• Relative coordinates
• generalized coordinates
• Cartesian co-ordinates
• Lagrange’ s equations and other approaches
• Differential equations (ODE) and differential algebraic equations (DAE)
• Co-ordinate partitioning and Lagrange multipliers
• Types of analyses (kinematic
• dynamic and linear dynamic)

Unit 4 Application of numerical methods

8 lecture hours

• NR method
• ODE integrators (Euler methods and Implicit methods)
• accuracy and Dahlquist’s tradeoff criteria
• Stiffness and damping - physical vs numerical
• bifurcation and singularities

Unit 5 Flexible Multibody Systems

• Dynamic analyses using classical approximation