Description

Analytical dynamics develops Newtonian mechanics to the stage where powerful mathematical techniques can be used to determine the behavior of many physical systems. The mathematical framework also plays a role in the formulation of modern quantum and relativity theories. Topics studied are the kinematics of frames of reference (including rotating frames), dynamics of systems of particles, Lagrangian and Hamiltonian dynamics and rigid body dynamics. The emphasis is both on the formal development of the theory and also use of theory in solving actual physical problems.
Learning Outcomes

Upon successful completion of this course, the student will be able to:

1. Distinguish kinematic and kinetic motion.

2. Identify the basic relations between distance, time, velocity, and acceleration.

3. Apply vector mechanics as a tool for solving kinematic problems.

4. Create a schematic drawing of a real-world mechanism.

5. Determine the degrees-of-freedom (mobility) of a mechanism.

6. Use graphical and analytic methods to study the motion of a planar mechanism.

7. Use computer software to study the motion of a mechanis

Contents

1. Generalized coordinates, Constraints, Degree of freedom
2. D’Alembert principle, Holonomic and non-Holonomic systems
3. Hamilton’s principle, Derivation of Lagrange equation from Hamilton’s principle
4. Derivation of Hamilton’s equation from a variational principle
5. Equations and Examples of Gauge transformations
6. Equations and examples of canonical transformations
7. Orthogonal Point transformations
8. The Principle of Least Action
9. Applications of Hamilton’s equation to central force problems, Applications to Harmonic oscillator
10. Hamiltonian formulism, Lagrange bracket and Poisson brackets with application
11. The Hamilton Jacobi theory, Hamilton Jacobi Theorem
12. The Hamilton Jacobi equation for Hamilton characteristic functions
13. Bilinear co-variant
14. Quasi coordinates, trans positional relations for Quasi coordinates
15. Lagrange’s equation for Quasi coordinates, Appel’s equation for quasi coordinates
16. Whittaker equation with applications
17. Chaplygian system and Chaplygian equation. 

Recommended Books

1. D.T. Greenwood. Classical Dynamics. (Prentice-Hall, Inc. 1965)
2. Chorlton F. Textbook of Dynamics (Van Nostrand).
3. Chester W. Mechanics (George Allen and Unwin Ltd, London)
4. Goldstein H. Classical Mechanics (Cambridge, Mass Addison-Wesely)
5. L.A. Pars, Treatise of Analytical Dynamics. (Heimann Press, London)
6. K. Sankara Rao, Classical Mechanics (Asoka K. Ghosh. 2015)
7. P.V. Panat, Classical Mechanics (Narosa Publishing House Delhi, 2005)

Suggested Books

1. D.T. Greenwood. Classical Dynamics. (Prentice-Hall, Inc. 1965)
2. K. Sankara Rao, Classical Mechanics (Asoka K. Ghosh. 2015)
3. D. A. Wells Lagrangian Dynamics (Schaum's outlines)

Reserah Products / Practicals /Labs /Assignments

Exercises are given as assignments to student to check their level of understanding.

Assignments 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

BS Math (Reg)

Tuesday                                                                                   9:30 -11;00 am 

Thursday                                                                                 11;00 am-12:30 pm

BS Math (SS)

Monday                                                                                   3:30 - 5;00 pm 

Thursday                                                                                 12;30 -2:00 pm

BS Math (Ex-PPP Campuse)

Monday                                                                                     12:30 - 2;00 pm

Wednesdy                                                                                9;30 - 11:00 am

MSc Math (Reg)

Thursday                                                                                  8:00-9;20 am

Friday                                                                                        8:00 -9;30 am

MSc Math (SS)

Thursday                                                                                  12:30-2;00 pm

Friday                                                                                        2:00 -3;30 pm

Commencement of Classes                                                   October 12, 2020

Mid Term Examination                                                            December 14-18, 2020

Final Term Examination                                                          February 08-12, 2021

Declaration of Result                                                              Februray 19, 2021