John R. Ray

Lagrangians and Systems They Describe-How Not to Treat Dissipation in Quantum Mechanics.

A Lagrangian that yields equations of motion for a damped simple harmonic oscillator is shown not to describe this system, but a completely different physical system. Thus, we have a simple counterexample to the statement: ’’If a Lagrangian gives the correct equations of motion for a given system then the Lagrangian describes the system.’’ We also construct a physical system that the Lagrangian describes and derive some of its properties. The quantum theory based on the above Lagrangian has been used to attempt to discuss the quantum theory of dissipation. This is, however, incorrect since the system the Lagrangian describes has no dissipation.

Bohlin’s and other integrals for the damped harmonic oscillator

We discuss several little known and interesting integrals of the motion for the damped harmonic oscillator.

Nonholonomic Constraints and Gauss's Principle of Least Constraint

The form of the equations of motion for a mechanical system subjected to nonholonomic constraints is discussed. A modified form of Gausss principle of least constraint is used to derive the equations of motion for systems with nonlinear, nonholonomic constraints. Other derivations of these same equations of motion are discussed.

Principle of equivalence

The principle of equivalence is discussed in its modern form based oin the theory of general relativity. This is compared to the original formulation of the princple in 1911.

Pressure fluctuations in statistical physics

We present a detailed discussion of pressure and pressure fluctuations in statistical physics. Among items discussed are the dependence of pressure fluctuations on the wall potential and the existence of a nonthermodynamic quantity in the pressure fluctuation formula.

Modified Hamilton's Principle

It is proven that the modified Hamiltons principle, in which both the coordinates and momenta are varied independently, can be derived from Hamiltons principle in which only the coordinates are varied independently.