Motion in Central Field
In this chapter we shall discuss the problem of bodies moving under the influence of central force. We shall attempt to explore the problem as throughly as is possible with the tools already developed.
- Motion in central force field
- Motion in arbitrary potential field
- Equation of orbits
- Kepler’s laws of planetary motion
Elastic and Inelastic Collision
In this chapter we shell discuss the problem related to the collision of bodies. We discuss one and two dimensional elastic and inelastic, both types of collision.
- Collision of particles
- Cross section
- Rutherford scattering
Elementary Principles
In this chapter we shall outline the applications of present day interest in physics. Basic to any presenttion of mechanics are a number of fundamental physical concepts, such as space, time, simultaneity, mass and force. these concepts will be analysed here critically.
- Generalized notations, eg., coordinate, velocity, acceeration, etc.
- Generalized momentum, force,potential
- D’Alembert’s principle and lagrange’s equations
Variational Principles and Lagrange’s Equations
In this chapter we discuss the appraach of variational principle to describe the motion of particle.
- Calculus of variations
- Hamilton’s principle and derivation of Lagrange’s equation
- Method of Lagrange undetermined multipliers
- Conservation theorems and symmetry properties
- Energy function and the conservation of energy
Inertial Frames
In this chapter we shell review properties and effect of moving coordinate system. We also discuss few examples of moving coordinate system.
- Moving co-ordinate system
- translating and rotating coordinate systems
- Coriolis force
- Foucault pendulum
Motion of Rigid Bodies
In this chapter we shall discuss the kinematical tools needed in the discussion of rigid body motion. In addition, the method of orthogonal transformations and the associated matrix algebra provides a powerful and elegent technique for investigating the characteristics of rigid body motion.
- Motion of rigid body
- Euler’s theorem
- Euler’s equation of motion
- Eulerian angle
- Symmetrical top
Relativity
In this chapter we shall review the assumptions of special theory of relativity and the consequences of these assumptions. Then, we also examine the formalism of the geometric picture of space-time.
- Gallilean transformation
- Non-inertial frame and fictitious force
- Lorentz transformation, length contraction, time dilation
- Addition of velocities
- Variation of mass with velocity
- Mass energy relation
- transformation of energy and momentum