Notes 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 3 years ago Flag 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 ...