Notes Angular momentum and Kinetic of motion about a point Angular momentum is the rotational analog of linear momentum. The angular momentum of a rigid body with one end fixed about the instantaneous axis through the fixed point is given ...

Notes Effect of coriolis force on a projectile shot along the earth's surface Let P be a point on the surface of the earth at latitude λ. Consider a rectangular Cartesian coordinate system with its origin rapidly fixed to earth at P. The ...

Notes Equation of motion of a spherical pendulum using Lagrange's equation of motion. A pendulum in which bob is constrained to move on a sphere rather than on a circle is called spherical pendulum. The position of the bob is located by spherical ...

Notes Lagrangian for a simple pendulum and equation describing its motion The angle θ between rest position and deflected position is chosen as generalized coordinate. If the string is of length l, then kinetic energy iswhere m is the ...

Notes Conservation of energy (Jacobi's integral) Consider a system of particles in a conservation force field and that the constraints do not change with time. Then,Total energy of the conservation system is constant. Thus Lagrangian ...

Notes Hamiltonian for a particle in a central force field and obtaining equation of motion of the particle In a central force field, force is always directed towards the centre. Potential energy is conservative so that Hamiltonian represents the total energy.As the motion is always confined in ...

Notes Hamilton-Jacobi Theory Canonical transformations may be used to provide a general procedure for solving mechanical problems. Two methods have been suggested. If the Hamilton is conserved, the solution could be obtained by …