Details of PH3101 (Autumn 2012)

Level: 3 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
PH3101 Classical Mechanics II Golam Mortuza Hossain

Syllabus
Free and constrained systems. Classification of constraints. Actual and virtual displacements. Ideal constraints. Principle of virtual work and D'Alembert's principle.



Generalized coordinates. Generalized forces. Lagrange's equation for Potential forces. Applications to simple systems. Conservation laws. The geometry of the tangent bundle . Dynamics on TQ.



The Jacobi function and the Hamiltonian. Legendre transformations. Hamilton's canonical equations. Poisson brackets. The cotangent bundle. Canonical transformations. Liouville's theorem.



The variational principle and Lagrange's equations.



Rigid body dynamics. Euler angles. The Euler equations of motion. Torque free rigid body motion. The heavy symmetric top.



Small oscillations. Normal modes and coordinates.



Scattering by central forces. The differential cross section for Rutherford scattering.



Nonlinear dynamics. The driven quartic oscillator.Stability of autonomous and non-autonomous systems. The Poincare-Bendixon theorem. The Poincare map. Chaos in the logistic map and other simple dynamical systems.





References

  1. L.. D. Landau and E. M. Lifschitz, Course on theoretical physics Vol. 1 : Mechanics, Butterworth-Heinemann, London (1998).

  2. F. Gantmacher, Lectures in Analytical Mechanics, translated by G. Yankovsky, Mir Publishers, Moscow (1975).

  3. H. Goldstein, C. Poole and J. Safko, Classical Mechanics, Pearson (2002).

  4. J. V. Jose and E.J. Saletan, Classical dynamics - a contemporary approach, Cambridge University Press, Cambridge (1998).

  5. V.I. Arnold, Mathematical methods of classical mechanics, translated by K. Vogtmann and A. Weinstein, Springer, Berlin (1981).









Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Core
2 IP 3 Not Allowed
3 MS 5 Core
4 RS 1 Not Allowed