# Analytical Dynamics: Course Contents (MAT 459)

In classical mechanics, analytical dynamics, or more briefly dynamics, is concerned about the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies.

## Course Objective

At the end of this course the students will be able to understand the fundamental principles of analytical dynamics, to study and apply Hamiltonian principle, Poisson bracket. Further they would be able to study different type of vibrations in strings and solve resuling mathematical equations.

## Course Contents

Constraints, generalized co-ordinates, generalized forces, General equation of dynamics, Lagranges equations, Conservation laws, Ignorable co-ordinates, Explicit form of Lagranges equation in terms of tensors. Hamiltons principle, Principle of least action, Hamiltons equations of motion, Hamilton-Jacobi Method. Poisson Brackets (P.Bs); Poissons theorem; Solution of mechanical problems by algebraic technique based on (P.Bs). Small oscilations and normal modes, Vibrations of strings, Transverse vibrations, Normal modes, Forced vibrations and damping, Reflection and transmission at a discontinuity, Longitudinal vibrations, Rayleigh’s principle.