Abstract
A simple graphical method for integrating the equation of motion of a particle in any field of force is used as a short laboratory exercise in an introductory course in mechanics. No knowledge of calculus nor differential equations is required of the student. Based directly on the vector definitions of average velocity and acceleration, and on central differences, it is capable of reasonable precision with relatively large steps. Using the three numbers, 6560cm3 = r2a(2τ)2, 53.7 cm = x1 = x−1, and 4.5 cm = y1 = −y−1, the student can develop half an elliptical orbit in 10 steps to about 6% accuracy on a 56 by 86-cm paper sheet in about one hour, and he can see for himself the step-by-step progress of a particle in an inverse-square field. The considerations leading to these or similar numbers are discussed briefly.
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