Notes Legrendre Transformation In Lagrangian formulation,The partial derivative of L with respect to qi means a derivative taken with all q's and q̇ 's constant. But in Hamilton's principle (Hamilton's approach) q's ...

Notes Kepler's problem by H-J method Kepler's problem is basically a problem related to central force. For simplicity we take inverse square force between nucleus of charge 'Ze' and electron of charge 'e'. One of the ...

Notes Poisson Bracket ELI5: Imagine you have a big toy box filled with different toys like cars, dolls, action figures, etc. Each toy represents a different thing, like the position and speed of ...

Notes Poisson's Second Theorem Statement: '' The poisson bracket of two constant of motion is itself a constant of motion.''If u and v are constant of motions then their poisson's bracket is also ...

Notes Freely falling particle using the H-J method To determine the motion of a particle falling vertically in a uniform gravitational field, the Hamiltonian is given byH = T + V = p²/ 2m + mgy .........1...

Notes Free vibrations of a linear triatomic molecule Fig: Model of a linear symmetric triatomicLet us consider two atoms of mass m are symmetric triatomic located on each side of an atom of mass M. All three ...

Notes The principle of least action The notion of least action is a key concept in the Hamiltonian formulation. This is a more general kind of path variation where time and coordinates for position are both ...

Notes Force free motion of a symmetrical rigid body Let us choose the symmetry axis as the principle z axis, so that I1 = I2 and Euler's equations simplifies towhere A is some constant and we have chosen ...