Notes Fourier series In mathematics, a Fourier series is a way to represent a periodic function as the sum of simple sine and cosine functions. It is named after Joseph Fourier, who introduced ...

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 + Vwhere y axis is taken as ...

Notes Introduction to continuous systems and fields Certain mechanical issues require a continuous system. For instance, consider the issue of an elastic solid that is vibrating. Here, the oscillation is caused by each point of the continuous ...

Notes Entropy of a classical ideal gas using the concept of microcannonical ensemble Consider a microcannonical ensemble for a system of 'N' non interacting point particles of mass M confined in a volume 'V' with total energy △E and E.The volume of ...

Notes Gibb's paradox and its resolution The entropy of the system is a measure of the disorder of the gas. We know, for the entropy of a classical ideal gas isConsider two perfect gas N1 ...

Notes Cannonical Ensemble The microcannonical ensemble is a general statistical tool but it is often very difficult to use practice because of difficulty in evaluating the volume of phase space. Hence cannonical ensemble ...