Variational Method and Its Application

The present book deals with two programs: one calculus of variations and one is Brackets. Calculation of variation is a major branch of analysis for a wide variety of problems in Mathematics and Mathematical Physics. It's a powerful technique for solving the problem of dynamics of rigid body, Optimization of orbits, Vibration Problem and Non-linear differential equation. Brackets are a powerful and sophisticated tool in Classical Mechanics particularly in Hamiltonian formalism. It is a way of characterization of Canonical Transformations by using an operation, known as brackets [Lagrange and Poisson bracket]. It is a powerful geometrical structure on the phase space. Basically, it is a mapping which maps two functions into a new function. Reformulation of classical mechanics is indeed possible in terms of brackets. It provides a direct link between classical and quantum mechanics. Generalized Coordinates, Lagrange equation of motion, Canonical Transformation and Geometrical equations are included. The Lagrangian for some of coupled non-linear partial differential equations are cited.