E-ISBN: Publication Year: 2004
Binding: Paper Back Dimension: 160mm x 240mm Weight: 280
About the book
Beginning with the formula used to derive Euler dynamical equations which relates rate of change of a vector with time with reference to the fixed frame to that in a rotating frame, along with its preliminaries and applications the book discusses Eulerian, Lagrangian and Hamiltonian approaches to generalized motion on rigid body in sequential chapters, emphasizing how one approach was extended and simplified by other one. The last chapter deals with canonical transformations from one phase space to other one, and invariance of certain properties including Poisson beackerts.
A lot of problems • Miscellaneous exercises • Glossary
Table of Contents
Chapter One - Motion in a Rotating Frame of Referenes: Rotation of a vector in two and three dimensional frames / Velocity and Acceleration components in two dimensional polar and intrinsic coordinates / Motion of a particle in two and three dimensional rotating frames / Effect of the Earth rotation on particle’s motion / Effect of Coriolis force on some natural events like river, cyclones, trade winds / Motion of Rigid Body in rotating frame / Chapter Two: Eulerian Approach to Motion of Rigid Body about a Fixed Point: Kinetic Energy, Angular momentum of a Rotating Body / Euler’s dynamical equations of motion / Euler’s geometrical equations of motion / 10 solved questions preceeded by some standard results / Chapter Three: Lagrangian Approach to Rigid Body Motion: Lagrangian Approach being single approach to Linear and Rotational motion both / Generalised coordinates, momenta and forces / Lagrange equations of constrained motion for finite forces / Energy equation / Verification of ten known dynamic problems / Solutions of 7 unsolved questions of Dynamics II - Ramsay / Lagrange Equation of motion for impulses / Solutions of 4 unsolved questions of Dynamics II - Ramsay / Smal oscillations with solutions of 8 unsolved questions from Dynamics II - Ramsay / Chapter Four: Hamiltonian Approach to Rigid Body Motion: Hamilton’s equations of motion / Verifications of 10 known dynamic problems / Hamilton principle and principle of least Action / Hamilton Jacobi Equation of Motion / Hamilton Jacobi Theorem and its Verification for Known results of Projectile and Central Orbit / Chapter Five: Cononical Transformations and Pioson’s Bracket: The condition for a transformations to be Canonical / Generating Function and Symmetric Relations / Phase space and Elementary Volume and its Invariance under CT / CTs as a Group / Poisson Bracket and its properties / First and second theorems of Poisson’s Bracket / LIOUVILLE’s theorem / Inveriance of Poisson’s Bracket under Canonical Transformations / Ten solved problems on Canonical transformations