Classical Mechanics

Paper Code: 
24PHY121
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

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.
  • develop ability to differentiate between problems of classical and quantum nature and apply classical methods to solve the relevant problems.

 

Course Outcomes: 

 

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24PHY121

Classical Mechanics

(Theory)

 

 

 

 

 

 

CO1: Solve the basic concepts of coordinate systems and degrees of freedom and apply on various problems.

CO2: Develop Hamilton's and Lagrange's Equations using calculus of variation and apply them to solve problems of mechanics.

CO3: Determine the Conservation principles, Noether's theorem, Eulerian angles and Euler’s theorem and apply to solve these concepts to relevant problems. 

CO4: Justify and create Lagrange's-  Poisson’s brackets and Canonical transformation then analyze their relations.

CO5: Solve the Action angle variables, Lagrangian formulation and their applications.

CO6: 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

 

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment 

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24PHY121

Classical Mechanics

(Theory)

 

 

 

 

 

 

CO1: Solve the basic concepts of coordinate systems and degrees of freedom and apply on various problems.

CO2: Develop Hamilton's and Lagrange's Equations using calculus of variation and apply them to solve problems of mechanics.

CO3: Determine the Conservation principles, Noether's theorem, Eulerian angles and Euler’s theorem and apply to solve these concepts to relevant problems. 

CO4: Justify and create Lagrange's-  Poisson’s brackets and Canonical transformation then analyze their relations.

CO5: Solve the Action angle variables, Lagrangian formulation and their applications.

CO6: 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.

Essential Readings: 
  • “Classical Mechanics”, Goldstein, Addison Wesley.
  • “Classical Mechanics” J.C.  Upadhyaya, Himalaya Publishing House.
     
References: 
  • “Mechanics-VolumeI”,Landau.AndLifshiz. 
  • “ClassicalMechanics”,A.Raychoudhary.
  • “Classical Mechanics” N.C. Rana and P.S. Joag, Tata Mc Graw Hill
Academic Year: