Classical Mechanics (Theory)

Paper Code: 
24DPHY711
Credits: 
04
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 
Course Objectives: 
This course will enable the students to -
• apply knowledge to calculate the Calculus of variation and its application to simple problems, formulation of Lagrangian and Hamiltonian for a problem, Canonical transformation and Action angle variable.
• acquire ability to differentiate between problems of classical and quantum nature and apply classical methods to solve the relevant problems. 
 
Course Outcomes: 

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

 

 

 

 

 

24DPHY711

Classical Mechanics (Theory)

 

 

 

 

 

 

CO158: Solve the basic concepts of coordinate systems and degrees of freedom and apply on various problems.

CO159: Develop Hamilton's and Lagrange's Equations using calculus of variation and apply them to solve problems of mechanics.

CO160: Determine the Conservation principles, Noether's theorem, Eulerian angles and Euler’s theorem and apply to solve these concepts to relevant problems.

CO161: Justify and create Lagrange's-  Poisson’s brackets and Canonical transformation then analyze their relations.

CO162: Solve the Action angle variables, Lagrangian formulation and their applications.

CO163: Contribute effectively in Course specific interaction.

Approach in teaching:

 

Interactive Lectures, Discussion, problem solving in Tutorials,  Demonstration

 

Learning activities for the students:

Self learning assignments, Effective questions, Simulation, Seminar presentation, Solving numerical.

 

 

 

Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations

 

 

 

12.00
Unit I: 
Generalized Coordinate Systems and Principles

Basic concepts of coordinate systems and degrees of freedom; Holonomic and non-holonomic constraints; D-Alembert's Principle; Generalized coordinates; Principle of virtual work;Lagrangian, Lagrange's equation and its applications; Velocity dependent potential in Lagrangian formulation; Generalized momentum; Hamilton's Principle; Lagrange’s equation from Hamilton's Principle.

12.00
Unit II: 
Calculus of Variation and its Application
Calculus of variation and its application to simple problems: Hamilton's Equations; Applications of Hamilton’s equation; Hamilton’s canonical equation in different coordinate systems; Calculus of Variation and Euler-Lagrange’s equations; Brachistochrone Problem; Derivation of Lagrange's and Hamilton’s canonical equation from Hamilton’s variational principle; Method of Lagrange's undetermined multipliers; Principle  of least action.
 
11.00
Unit III: 
Conservation Principle and Euler’s equations
Conservation principle and Noether's theorem; Conservation of energy, linear momentum and angular momentum as a consequence of homogeneity of time and space and isotropy of space respectively.
Eulerian angles; Euler’s theorem; Angular momentum and Inertia Tensor; Euler’s equations; Euler’s equation of motion for a rigid body.Levels of biological diversity: genetic, species and ecosystem diversity 
13.00
Unit IV: 
Canonical transformation:
Legendre transformations; Generating functions;Conditions for Canonical transformation; Bilinear invariant conditions; Lagrange's and Poisson’s brackets and their relations; Angular momentum and Poisson Brackets; equation of motion in Poisson bracket formulation; Invariance of Poisson’s and Lagrange’s Brackets under canonical transformations; Liouville's theorem. 
 
12.00
Unit V: 
Action angle variable:
Hamilton Jacobi equation and its applications; adiabatic invariance of action variable; The Kepler problem in action angle variables; theory of small oscillations in Lagrangian formulation; theory of small oscillations in normal coordinates and normal modes; Two coupled oscillator and solution of its differential equation; Two coupled pendulum; Double pendulum.
 
Academic Year: 
2024-2025
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