Course

Unit 1

Constrained Motion: Constraints, Classification of Constraints, Principal of Virtual Work, DAlemberts principal and its applications.

Unit 2

Lagrangian formulation: Generalized coordinates, Langrange’s equations of motion, properties of kinetic energy function, theorem on total energy, generalized momenta, cyclic-coordinates, integrals of motion, Jacobi integrals and energy conservation, Concept of symmetry, invariance under Galilean transformation, velocity dependent potential

Unit 3

Hamilton’s formulation: Hamilton’s function and Hamilton’s equation of motion, configuration space, phase space and state space, Lagrangian and Hamiltonian of relativistic particles and light rays.

Unit 4

Canonical Transformations: Generating function, Conditions for canonical transformation and problem. Poisson Brackets: Definition, Identities, Poisson theorem, Jacobi-Poisson theorem, Jacobi identity,(Statement only), invariance of PB under canonical transformation.

Unit 5

Central Force Problem:

Kepler’s laws, Orbital Dynamics, Stability

Rotational Motion:

Rotating frames of reference, inertial forces in rotating frames, Larmour precision, electromagnetic analogy of inertial forces, effects of Coriolis force, Focoult’s pendulum.

Text Books / References

Text Books:

• Goldstein, Classical Mechanics, Addison — Wesly, 2E, 1980.

Reference Books:

1. Landau and Lifshitz, Mechanics, Butterworth-Heinemann, 3, 1976
2. S T Thornton and J B Marion, Classical Dynamics of Particles and Systems, Brooks Cole, lE, 2009
3. Walter Greiner, Classical Mechanics: Systems of Particle and Hamiltonian Dynamics, Springer — Verlag, lE, 2004

• Col Understand the basic conservation laws in physics and the concept of phase portrait
• CO2 Understand and apply the Lagrangian formalism to simple dynamical systems
• CO3 Apply Hamilton’s equations and solve dynamical systems
• CO4 Apply the properties of Poisson’s bracket and canonical transformations for solving simple systems
• CO5 Apply the theory of Rigid body dynamics and analyze the motion of rigid bodies
• CO6 Apply small oscillation theory developed in getting the frequencies of different of modes of oscillations in a coupled systems