PHY 254 — CLASSICAL MECHANICS II
BSc BSc Physics · Kwame Nkrumah University of Science and Technology
The Lagrangian equation and their application to the solution of more small-oscillation problems. Conservation theorems and symmetry properties: Generalised coordinates and momenta; cyclic or ignorable coordinates; conservation of the generalised momentum conjugate to a cyclic coordinate; conservation of total energy for conservative systems. The concept of the Hamiltonian. The two-body central force problem; reduction to the equivalent one-body problem. The equations of motion and first integrals. The equivalent one-dimensional problem and classification of orbits. The differential equation for the orbit and integrable power-law potentials. The Kepler problem. Scattering in a central force field. Frames of reference; inertial frames; the principle of relativity. The Galilean transformation and its limitations. The Lorentz transformatio. Proper time; time dilation; the Lorentz-Sitzgerald. contraction. Addition of velocities. Covariant four-dimensional formation of STR; 4 – vectors and relativistic invariants. Generalization of Newton’s equations of motion. The Minkorski force. Relativistic momentum, energy and mass. Einstein’s relation. Legendre transformations. Derivation of Hamilton’s canonical equations. Application to simple problems. Cyclic coordinates and Routh’s procedure. Conservation theorems and the physical significance of the Hamiltonian.
- Credits
- 2
- Level
- Level 200
Other courses on this programme
- FC 281 — FRENCH FOR COMMUNICATION III
- FC 282 — FRENCH FOR COMMUNICATION IV
- PHY 251 — ELECTRONICS I
- PHY 252 — ELECTRONICS II
- PHY 253 — CLASSICAL MECHANICS I
- PHY 255 — THERMODYNAMICS
- PHY 256 — E.M. THEORY
- PHY 259 — MATHEMATICS FOR PHYSICS III
- PHY 260 — MATHEMATICS FOR PHYSICS IV
- PHY 261 — PROGRAMMING WITH PASCAL I
- PHY 262 — PROGRAMING WITH PASCAL II
- PHY 263 — NUCLEAR PHYSICS
Practising PHY 254 with Questora
Upload your own slides, notes and past papers for PHY 254 and Questora builds mock exams, practice questions and a revision plan from them.
Start freeCourse details from Courses for BSc. Physics - Physics.