Modeling Pitch Trajectories in Fastpitch Softball

The fourth-order Runge–Kutta method is used to numerically integrate the equations of motion for a fastpitch softball pitch and to create a model from which the trajectories of drop balls, rise balls and curve balls can be computed and displayed. By requiring these pitches to pass through the strike zone, and by assuming specific values for the initial speed, launch angle and height of each pitch, an upper limit on the lift coefficient can be predicted which agrees with experimental data. This approach also predicts the launch angles necessary to put rise balls, drop balls and curve balls in the strike zone, as well as a value of the drag coefficient that agrees with experimental data. Finally, Adair’s analysis of a batter’s swing is used to compare pitches that look similar to a batter starting her swing, yet which diverge before reaching the home plate, to predict when she is likely to miss or foul the ball

Two Examples of Circular Motion for Introductory Courses in Relativity

The circular twin paradox and Thomas Precession are presented in a way that makes both accessible to students in introductory relativity courses. Both are discussed by examining what happens during travel around a polygon and then in the limit as the polygon tends to a circle. Since relativistic predictions based on these examples can be verified in experiments with macroscopic objects such as atomic clocks and the gyroscopes on Gravity Probe B, they are particularly convincing to introductory students.Comment: Accepted by the American Journal of Physics This version includes revision

Zur architektonischen Gestaltung von Zuhoereraeumen in warm-trockenen Klimaten unter Beruecksichtigung raumakustischer Bedingungen

Published in two volumesSIGLEAvailable from TIB Hannover: DW 5944 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman