Courses Detail Information

VM543 – Analytical Dynamics


Instructors:

Credits: 3 credits

Pre-requisites: Vm 440 Intermediate Dynamics and Vibration

Description:

Vectors and tensor. Scalar, vector and tensor products. Second order tensors. Coordinate systems. Differential geometry of curves, surfaces and three dimensional mappings. Basis principles of dynamics. Newton’s laws for particles and systems of particles. The geometric description of rotations. Euler angles. Time and spatial derivatives. Kinematics of rigid bodies. Kinetics of rigid bodies. Variational and energy principles in dynamics. Use of motion simulation and virtual prototyping software for multibody dynamics.

Course Topics:

Introduction to modeling in multibody dynamics and computer simulation

Scalar, vector & matrix operations; Various coordinates & unit vectors;

Simple rotation; Vector function & differentiation

Research project proposal presentation

Kinematics; Rotation transformation; finite rotations

Angular velocity & angular accelerations; Kinematics; Two points fixed on a rigid body

Kinematics: One point moving on a rigid body; Partial velocity and partial angular velocity

Mass center; Tensor; Inertia dyadic; Inertia matrix;

Parallel axes theorem; Principal axes; Principal plan;

Forces, moments & equivalent force systems;

Generalized active forces

Interaction forces; Bringing noncontributing forces into evident; Generalized inertia forces

Equations of motion: Newton-Euler method;

Equations of motion: Newton-Euler method;

Research project progress report & presentation

Equations of motion: Lagrange’s method;

Equations of motion: Lagrange’s method;

Equations of motion: Kane’s method; non-constrained systems

Equations of motion: Kane’s method; constrained systems

Numerical issues, computer simulation and virtual prototyping

Integration of CAD/CAE/CAM