ABSTRACT
The strategy of choosing a particular coordinate system or frame to perform a calculation or to present a concept is ubiquitous in both mathematics and physics. Sir Isaac Newton’s equations of planetary motion are much easier to solve in polar coordinates than in Cartesian coordinates. Many problems in introductory mechanics involve finding the trajectory of a particle under the influence of various forces and/or subject to certain constraints. To each independent variable in the coordinate system, one associates the unit vector that corresponds to the directions of change with respect to that variable. In the study of trajectories, whether in physics or geometry, it is often convenient to use a frame that is different from the Cartesian frame. Changing types of frames sometimes makes difficult integrals tractable or makes certain difficult differential equations manageable. Though an absolute frame arises naturally in the mental framework of Cartesian coordinates, to assume the existence of an absolute frame in physical systems poses serious challenges.
