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 D'Alembert's principle Consider a system in equilibrium, i.e. total force Fi on every particle is zero. Then work done by this force in a small virtual displacement δr will also vanish i.e., ...

Notes Cannonical transformation Transformation: A given system can be described by more than one set of generalized coordinates. We can choose a set which is most convenient for the solution of the problem ...

Notes Lagrangian and Hamiltonian formulation for continuous system and fields. Many of the systems can be described as continuous system in the sense that various properties are continuous functions of the coordinates. For example, the mass of the system may ...

Notes Physical Significance of Hamiltonian Like Lagrangian, H also posses the dimensions of energy but in all circumstances it is not equal to the total energy E. Restriction for this equality, i.e., E= H are:...