Notes Angular momentum and Kinetic energy of motion about a point Angular momentum is a measure of the rotational motion of an object around an axis or a point. It is defined as the product of the moment of inertia (a ...
Notes Effect of coriolis force on a projectile shot along the earth's surface Let P represent a location on the earth's surface at latitude λ. Take into account a rectangular Cartesian coordinate system with P as the swiftly fixed origin. The system's z ...
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 Euler's theorem A rigid body is capable of two independent motions: rotation and translation. The position and orientation of such a body in motion can therefore be fully described. Three of these ...
Notes Cannonical transformation Transformation: More than one set of generalized coordinates can be used to describe a given system. We can decide on a set that will make solving the problem at hand ...
Notes Physical Significance of Hamiltonian The Hamiltonian in classical and quantum mechanics is a mathematical object that encodes the total energy of a physical system. It plays a central role in determining the time evolution ...
