### Classical Mechanics MATH-302

Description

To provide solid understanding of classical mechanics and enable the students to use this understanding while studying courses on quantum mechanics, statistical mechanics, electromagnetism, fluid dynamics, space-flight dynamics and continuum mechanics.

Pre Requisites

Vector Analysis & Mechanics

Learning Outcomes

In the end of this course, students will be able to understand a set of core concepts—space, time, mass, force, momentum, torque, and angular momentum in order to solve the most famous physics problem, the motion of the planets.

Contents

1. Differential operators and its applications in classical motion,
2. Curvilinear coordinates and motion of particles, rectangular components of velocity and acceleration,
3. Line integrals and motion of particles in streaming, applications of del. operator to classical motion,
4. Curl, divergence and gradients for the motion of particles,
5. Surface and volume integrals in the streaming of particles,
6. Gauss and Stokes theorem with significance,
7. Green’s theorem and its applications,
8.  Green’s 1st and 2nd identity with related integrals,
9. Central Forces and Planetary Motion: Central force fields, equations of motion, potential energy,
10. Classical theory in planetary motion and law of inertia,
11. Motion in an inverse square field. Planer Motion of Rigid Bodies: Introduction to Rigid bodies,
12. Translations, rotations. Linear and angular velocity of a rigid body about a fixed axis,
13. Moments and products of inertia. Parallel and perpendicular axis theorem,
14. Motion of Rigid Bodies in Three Dimensions: General motion of rigid bodies in space,
15. Angular momentum and moment of inertia. Principal axes and principal moments of inertia,
16. Determination of principal axes by diagonal zing the inertia matrix. Equimomental systems,
17. Euler Equations of Motion of a Rigid Body: Rotating axes theorem. Euler’s dynamical equations,
18. Free rotation of rigid body with three different principal moments, torque free motion of a symmetrical top and rotational kinetic energy,
19. The Euler angles, angular velocity and kinetic energy in terms of Euler angles.

Recommended Books

1. K.L. Mir, Theoretical Mechanics (Ilmi Ketab Khana, Lahore, 2007).
2. K.R. Sankara, Classical Mechanics (Prentice Hall of India, New Dehli, 2005).

Suggested Books

1     R. Murray Spiegel, Vector Analysis and an Introduction to Tensor Analysis (Schaum’s outlines, 1980).

Assessment Criteria

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

Key Dates and Time of Class Meeting

Monday & Tuesday                             03:30 PM-05:00 PM (BS-VI Ex-PPP)

Tuesday & Wednesday                       08:00 AM-09:30 PM (BS-VI Regular)

Wednesday & Thursday                      12:30 PM-02:00 PM & 03:30 PM-05:00 PM (BS-VI BS-VI Self Support)

Commencement of Classes                                              January 13, 2020

Mid Term Examination                                                    March 09-13, 2020

Final Term Examination                                                   May 04-08, 2020

Declaration of Result                                                        May 19, 2020