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Course Contents

The free particle, constraints, Dynamical system, Th fundamental equations,Frames of reference, Newton’s laws of motion, Conservation laws, Constraints, generalized coordinates, Virtual work, D’Alembert’s principle, Lagrange’s equations, Quasi coordinates, Maggis equation, Lagrange-Hamel equation, Routhian function, Conservative systems, Liouville's system, Hamilton’s principle, Generalized momenta and phase space, First integrals of motion and cyclic coordinates, Hamilton’s equations of motion, Hamilton’s equations from variational principle, Principle of least action, Canonical transformation, Infinitesimal canonical transformations, The Lagrange and Poisson brackets, Hamilton-Jacobi equation, Hamilton’s characteristic function, Harmonic oscillator in the Hamilton-Jacobi method, Stability of motion, Impulsive motion


Course Learning Outcomes

The aim of this course is to understand the basics of the dynamics such as analysis of particle dynamics, rigid body application of laws of work-energy and Impulse-momentum in the dynamic analysis, information about the kinetic analysis of rigid bodies in three and above dimensions. The student will learn the Lagrangian and Hamiltonian formalism for the laws of motion, which are generalizations of Newton’s equations of motion and will be capable to apply the formalism of analytical dynamics to actual problems.


Review

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Constraints

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types of constraints

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Generalized coordinates

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Constraints and degree of freedom

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Equations of Motion

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Dynamical System

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frames of references_1

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frames of reference_2

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Conservation laws

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Principle of Virtual Work

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D’Alembert’s principle

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Lagrange’s equations

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HAMEL’S EQUATIONS

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Routhian function

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Conservative Systems

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Liouville's system

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Hamilton’s principle

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Generalized momenta and phase space

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First integrals of motion and cyclic coordinates

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Hamilton’s equations of motion

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Hamilton’s equations from variational principle

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Principle of least action

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Canonical transformation

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Infinitesimal canonical transformations

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The Poisson bracket

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The Lagrange bracket

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Hamilton-Jacobi equation

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Hamilton’s characteristic function and Harmonic oscillator

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Stability of motion

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Impulsive motion

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Book Title : Classical Dynamics
Author : Greenwood, D.T
Edition :
Publisher : Dover Publications



Book Title : Classical Mechanics
Author : Aruldhas, G
Edition :
Publisher : PHI Learning



Book Title : Analytical Dynamics Theory and Applications
Author : Mark D. Ardema
Edition : 1st
Publisher : Kluwer Academic / Plenum Publishers New York, Boston, Dordrecht, London, Moscow



Book Title : A Treatise on ANALYTICAL DYNAMICS
Author : L. A. PARS (President of Jesus College, Cambridge)
Edition : 1st
Publisher : Heinemann Educational Books Ltd (LONDON)
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Title : Analytical Dynamics Theory and Applications
Type : Reference Book

View Analytical Dynamics Theory and Applications