Nonlinear Dynamics: Phase Space

In the previous post in the series, we looked at the Dynamical systems. These systems are nonlinear and cannot be analyzed easily, the difficulty arising from the fact that most of them aren’t exactly solvable. By exactly solvable, we mean a

Variational Principle

The variational Principle(or Hamilton’s Principle), as proposed by Hamilton is also known as the Law of Least Action. It is a fundamental principle of Mechanics and is more basic than Newton’s laws of motion. We have discussed D’Alembert’s Principle before

Generalized Coordinates

Generalized coordinates in classical mechanics are a way to describe the phase space configuration(relative to a reference) of a system. In simple words, these can be used to simplify description of a system by using a small set of (not

Kinematics : translational motion

Kinematics is the domain of Mechanics that deals with simple translational motion. In this domain, we simply discuss the relationships among displacement, velocity and acceleration; without considering the cause of the motion. We know that velocity is the rate of

Law of Universal Gravitation

Equation #9: Newton’s law of Universal Gravitation Probably the most familiar law in science which everyone seems to understand intuitively, the law of universal gravitation is one of the most powerful and useful equation for practical purposes. Before Newton, people