Classical Mechanics Course Research Articles

Pattern Formation by Inelastic Collisions, Especially in Planetary Systems

The Titius–Bode law governs the planet distribution in our Solar system. In this paper a possible explanation is proposed based on inelastic collision effects among planetessimals during the evolution of the Solar system. The main purpose of this paper is, however, to introduce a strategy to study phenomena driven by rare but drastic events such as colllisions in the planetary problem. Many complex systems evolve through rare but violent events, so that an efficient strategy to simulate such systems is desirable. An event-driven strategy is proposed in this article, and is used to produce many runs of 108 year evolution history of planetary systems. I have found that the Titius–Bode law holds approximately, if the gravitational effect (scattering) and the collisions are taken into account. The result illustrates the importance of inelastic collisions, which are often neglected in the standard classical mechanics courses. Therefore, for completeness, other simpler particle systems under the effect of inelastc collisions, such as one-dimensional systems, are also included.

The Physical Pendulum in an Advanced Undergraduate Course in Mechanics

The physical pendulum treated with a Hamiltonian formulation is a natural topic for study in a course in advanced classical mechanics. For the past three years, we have been offering a series of problem sets studying this system numerically in our third-year undergraduate courses in mechanics. The problem sets investigate the physics of the pendulum in ways not easily accessible without computer technology and explore various algorithms for solving mechanics problems. Our computational physics is based on Mathematica with some C communicating with Mathematica, although nothing in this paper is dependent on that choice. We have nonetheless found this system, and particularly its graphics, to be a good one for use with undergraduates.

A final-exam comparison involving computer-based instruction

In an introductory classical mechanics course, the same final exams were given to 540 students taught in the usual way and to 486 students who received computer-based instruction. All students scored better on problems which had been made up by their own lecturer. Students in the computer-based course scored better overall. These statistically significant results are of interest not only for comparing the two forms of instruction but also for their implications on the use of exam scores for such comparisons.

A computer-based course in classical mechanics

A computer-based course in classical mechanics

Project Boomerang

The returning-type boomerang illustrates many of the principles of rigid body dynamics and some aerodynamic principles as well. Here is described an experimental project on boomerangs by members of an undergraduate course in classical mechanics. The students designed and made their own boomerangs, devised their own procedures, and carried out suitable measurements. Some of their data and a simple analysis for the two-bladed boomerang are presented in this article.

An Experiment in Teaching Applied Mathematics in an Australian University

This article describes an experiment in the teaching of an ‘Applied Mathematics’ course at the University of Melbourne. The syllabus covered was not that of the conventional classical mechanics course but included topics felt to be attractive to first‐year science undergraduates.

Some Developments in Generalized Classical Mechanics

The generalized classical mechanics of Borneas is extended to include familiar topics in an advanced course in classical mechanics. Hamilton's equations of motion are derived in a generalized form. Interesting features of momenta related to, but not conjugate to generalized cyclic coordinates are developed. Generalized Poisson and Lagrange brackets are defined and the subjects are developed. The inverse nature of generalized Poisson and Lagrange brackets is proved, and generalized equations of motion are expressed using Poisson bracket notation.