Notes Thermodynamics behaviour of an ideal gas of photons (black body radiation) Consider an electromagnetic radiator enclosed in a fixed volume 'V' at a fixed temperature T. One can obtain such a system by making a cavity in any material and then ...
Notes Grand Cannonical Ensemble Each system in the microcannonical ensemble has the same fixed energy and the same amount of particles (N, V, E). This ensemble's system is a closed, isolated thermodynamic system (because ...
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 ...
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 Hamilton's equation of motion from variational principle Hamilton's principle is stated as:Equation 1 is sometimes referred as the modified Hamilton's principle. This principle leads Hamilton's cannonical equations of motion as shown belowLabelling each of …
Notes Euler's angles The orientation of a rigid body must be specified by three independent factors in order for the associated orthogonal transformation matrix to have the determinant +1 and to be used ...
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 ...
Notes Condition for steady Precession of Heavy Symmetrical top with one point fixed Consider the motion of a heavy symmetrical top spinning about the axis of symmetry, viz z'axis. The top is subject to a gravitational torque and is locked at its lower ...
