Advanced Classical Mechanics

About this course

In this content - Advanced Classical Mechanics, we have started our discussion with particle motion under central force. This central force is a conservative irrotational force which always acts along the radial sense and it may be attractive or repulsive. Under action of this central force, the motion of the particle will become confined in a plane and the orbit of the particle must lie in two dimension. The motion will be restricted with energy and angular momentum conservation and here the best application of such central force problem is on the motion of planet and satellite. After that we have discussed the features of constrained motion where the motion is restricted by at least one or more than one condition or restriction. For such constrained motion, the corresponding constraint will be hold by the force of constraint which is itself no work force. Here a several conservative holonomic systems are made analyzed in this constrained motion. On the other hand, in this content, we have discussed the basic concept of Calculus of Variation as given by Euler and the concept is fully applied to the second generation of Classical Mechanics, known as Lagrangian Dynamics through the concept of Lagrangian of a holonomic conservative system by proper use of generalized coordinates and other generalized parameters.  Lagrange's equation of both 1st and 2nd kind are made developed in several way and then is applied to several conservative holonomic system. At the end of this content, the Hamiltonian of the system is made defined through Legendre dual transformation and after that Hamilton's canonical equations of Hamiltonian dynamics which is specifically 3rd generation of Classical Mechanics are obtained from basic characteristics of Hamiltonian and finally these canonical equations are made applied for analyzing several conservative systems.