Notes 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 …
