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