It's Obvious... Not: Charged Particle Motion in a Magnetic Field and Third Order Homgeneous Differential Equations
This installment of “It’s Obvious. Not!” looks at: Book: “Classical Dynamics of Particles and Systems” Edition: third Authors: Jerry B. Marion and Stephen T. Thornton Publisher: Harcourt Brace Jovanovich Page: 68 This post looks at Example 2.10 that investigates the motion of a charged particle in a magnetic field. The example is fairly straightforward with one exception. When determining the equations of motion, the authors propose a solution for the system of differential equations discussed below and reference example C.2 of Appendix C. It’s not immediately apparent how to use Example C.2 to arrive at the authors’ solution, so the steps are outlined in detail here. If you have questions, or suggestions, all comments are always welcome! The original system of coupled differential equations is: First, the authors’ differentiate both equations and then substitute the results into the other: at this point, the book suggests using the technique of ex...