Generalized brachistochrone problems in varying gravitational field and brachistochrone in a crossed EB field

Date

10-2004

Degree

Bachelor of Science in Applied Physics

College

College of Arts and Sciences (CAS)

Adviser/Committee Chair

Rogel Mari D. Sese

Abstract

We investigated generalizations of brachistochrone problems in varying gravitational field inside a solid homogeneous sphere and in a varying gravitational field due to a point mass. Further, we also covered an ideal brachistochrone problem for a charged particle in a crossed EB field from which we found out that the solution is a cycloid. In the generalizations, we considered the addition of dissipative forces to the ideal case where they are absent. These dissipative forces are dry friction as given by Coulomb-Amonton's law and fluid resistance that is directly proportional to the speed of the particle. For each problem involving varying gravitational field that we dealt with, a differential equation was derived and then numerically calculated. From these differential equations and numerical solutions, certain findings concerning the behavior of brachistochrones were made. For brachistochrones inside a solid homogeneous sphere, if the center of the homogenous sphere is located in the origin of polar coordinate system, our numerical solution is suggestive that for a particular value of the polar angle where the trajectories are existent, the greater is the strength of the dissipative force, the higher is the value of the polar coordinate r. On the other hand, for brachistochrones in a varying gravitational field due to a point mass, if the point mass where we attribute a varying gravitational field is located at the origin of polar coordinate system, then our numerical solution is suggestive of the same findings as in the brachistochrone inside a solid homogeneous sphere. Furthermore, for the brachistochrones in varying gravitational field, we found out that the trajectories terminate at a certain point before certain conditions that are related to the coefficients of dissipative force are met.

Language

English

Location

UPLB Main Library Special Collections Section (USCS)

Call Number

Thesis

Document Type

Thesis

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