Unit 1

Introduction to Lagrangian dynamics
Survey of principles, mechanics of particles, mechanics of system of particles, constraints, D’Alembert’s principle and Lagrange’s equation, simple applications of the Lagrangian formulation, variational principles and Lagrange’s equations, Hamilton’s principles, derivation of Lagrange’s equations from Hamilton’s principle, conservation theorems and symmetry properties.

Unit 2

Central field problem
Two body central force problem, reduction to the equivalent one body problem, Kepler problem, inverse square law of force, motion in time in Kepler’s problem, scattering in central force field, transformation of the scattering to laboratory system, Rutherford scattering, the three body problem.

Rotational kinematics and dynamics
Kinematics of rigid body motion, orthogonal transformation, Euler’s theorem on the motion of a rigid body.

Unit 3

Angular momentum and kinetic energy of motion about a point, Euler equations of motion, force free motion of rigid body.

Practical rigid body problems
Heavy symmetrical spinning top, satellite dynamics, torque-free motion, stability of torque-free motion – dual-spin spacecraft, satellite maneouvering and attitude control – coning maneuver – Yo-yo despin mechanism – gyroscopic attitude control, gravity- gradient stabilization.

• H. Goldstein, Classical Mechanics, Narosa Publishing House, New Delhi, 1980, (Second Edition)
• H. Goldstein, Charles Poole, John Safko, Classical Mechanics, Pearson education, 2002 (Third Edition)
• Howard D. Curtis, Orbital Mechanics for Engineering Students, Elsevier, pp.475 – 543
• Anderson John D, Modern Compressible flow, McGraw Hill.

Reference(s)

• D. A. Walls, Lagrangian Mechanics, Schaum Series, McGraw Hill, 1967.
• J. B. Marion and S. T. Thornton, Classical dynamics of particles and systems, Ft. Worth, TX: Saunders, 1995.

Evaluation Pattern

Course Outcomes

• CO1: Able to use the Lagrangian formalism to solve simple dynamical system
• CO2: Able to understand Hamiltonian formalism and apply this in solving dynamical systems
• CO3: Able to apply Lagrangian formalism in bound and scattered states with specific reference to Kepler’s laws and Scattering states
• CO4: Able to solve problems in the Centre of Mass frame and connect it to Laboratory Frame of Reference
• CO5: Understand and solve problems in rigid body rotations applying of Euler’s equations.

CO – PO Mapping