Analysis in the Classical Mechanics

Equations of motion with arbitrary potential fields are described by simple

formulas based on Newtonian law. However, they are generally complicated to solve.

This chapter presents several methods for deriving and solving equations of motion with

different coordinate systems.

Two-body motion is introduced based on the coordinates of the motion of the center of

mass and the relative motion. R elative motion perpendicular to a relative position is

discussed using angular momentum, wherein the temporal change is given by the torque.

The Lagrange equation is introduced for application to all types of coordinates. The polar

coordinate system is convenient for deriving an equation of motion with a spherically

symmetric potential because the angular momentum is constant. The motion in the radial

direction should be considered taking the centrifugal force potential into account. The

Lagrangian is also introduced with respect to electromagnetic fields.

Keywords: Angular momentum, Center of mass, Centrifugal force, Energy, Gravity, Kepler’s law, Lagrange equation, Momentum. Inertial moment, Newtonian mechanics, Relative motion.

Cite as

Current Physics

Advances in Classical Field Theory

Are We There Yet? The Search for a Theory of Everything

Atmospheric Flow Fields: Theory, Numerical Methods And Software Tools

Atomic Coherence and its Potential Applications

Classical Fluid Mechanics

Classical Mechanics and Quantum Mechanics: An Historic-Axiomatic Approach

Density Matrix Theories in Quantum Physics

Digital Signal Processing in Experimental Research Volume Title: Fast Transform Methods in Digital Signal Processing

Dynamical Processes In Atomic And Molecular Physics

Einstein's Revolution: A Study Of Theory Unification

Fundamentals of Analysis in Physics