### Classical Mechanics II

DESCRIPTION & OBJECTIVES: The aim of this course is to continue, merge and extend the studies of Classical Mechanics I PHYS-302 in previous semester. Its ideas also link with other courses like quantum mechanics and condensed matter. The fundamental goal of this course is to create understanding in students to classical mechanics and its applications. This course provides the students the up-to-date treatment of classical mechanical systems and serves as basics and pre-requisite of Quantum Mechanics so that students face least difficulty in entering from classical Physics to Quantum mechanics. The purpose of the course is to make the students capable in formulating and solving physics problems.

Learning Outcomes:

After completion of the course, students will be able

1- To deal with, central force motion and system of particles and related phenomenon.

2- To write the equations of motion for complicated mechanical systems using the Lagrange's and Hamilton's equations of motion.

3- To develop problem solving approach and critical thinking, Students will be able to solve problems in applied physics.

4- To start advance fields of Physics like quantum mechanics and field theory on the basis of Lagrangian and Hamiltonian technique.

CONTENTS:

Kinematics of system of particles, Collision between particles, centre of mass co-ordinate system, Elastic collision in LAB and CM coordinate system, scattering by central force field, Rutherford’s scattering formula, Limitations of Newtonian mechanics, Some methods in the calculus of variations, Euler’s equation, The “second form” of Euler’s equation, Generalized co-ordinates and constraints, Configuration space, D’ Alembert’s principle and Lagrange ‘s equation, Hamilton’s principle and Lagrange’s equation, Integrals of motion and conservative laws, Lagrangian versus Newtonian approach to classical mechanics, Hamiltonian of dynamical system, Hamilton’s canonical equations, Integrals of Hamilton’s equation, Canonical transformations, Poisson bracket and their properties, Central force motion, Two body problem and reduced mass, General solution of problems of motion in central force field, inverse square law of force, Kepler’s laws of planetary motion, Applications of central force motion, Orbital Dynamics, Orbits in central field and stability of circular orbits.

1. Classical dynamics of particles and systems by S. T. Thorntom and J. B. Marion, 5th. Edition Harcourt Brace and company (2012).

2. Classical Mechanics by Tai L. Chow, John Wiley & Sons (1995).

3. Classical Mechanics by H. Goldstein, 3rd. Edition. Addison Wesley, Reading, Massachusetts (1980).

ASSESSMENT CRITERIA

Sessional:

20 Marks (Home assignments 10 marks+ sessional tests 10 marks, Problems set assignment and sessional test will be conducted at the end of each chapter)

Mid Term exam: 30 marks

Final exam: 50 marks

RULES AND REGULATIONS:

At least class attendance of 75 % of the lectures delivered is mandatory for all students. Students must submit their home assignments at the scheduled time. Three marks out of ten marks from the home assignments may be assigned to attendance.

95-100 % attendance = 3 marks,

90-95 % attendance = 2 marks

80-90 % attendance = 1 mark

Class Timings:

M. Sc. II (Reg) Monday-Tuesday at 11.30 A.M.

M. Sc. II (SS) Monday-Tuesday at 03.30 P..M