A problem similar to the famous brachistochrone problem is examined in which, instead of a smooth curve, the path consists of two straight-line sections, one slant and one horizontal. The condition for minimum sliding time is investigated, producing results that are both counterintuitive and interesting.
References
[1]
Fox, C. (1963) An Introduction to the Calculus of Variations. Dover, New York, 24-25.
[2]
Mohazzabi, P. (1998) Isochronous Anharmonic Oscillations. Canadian Journal of Physics, 76, 645-657. https://doi.org/10.1139/p98-029
[3]
Webster, A.G. (1959) The Dynamics of Particles. 2nd Edition, Dover, New York, 144-148.
[4]
Huygens, C. (1673) Horologium Oscillatorium. https://iiif.library.cmu.edu/file/Posner_Files_531.1_H98H_1673/Posner_Files_531.1_H98H_1673.pdf
[5]
Lamb, H. (1961) Dynamics. 2nd Edition, Cambridge University Press, Cambridge, 110-112.
[6]
Fowles, G.R. and Cassiday, G.L. (1993) Analytical Mechanics. 5th Edition, Saunders College Publishing, New York, 142-143.
[7]
Herrick. D.L. (1996) Constant-Magnitude Acceleration on a Curved Path. PhysicsTeacher, 34, 306-307. https://doi.org/10.1119/1.2344445
[8]
Fowler, M. (1996) Sliding down a Cycloid.PhysicsTeacher, 34, 326. https://doi.org/10.1119/1.2344459
[9]
Halliday, D., Resnick, R. and Walker, J. (2011) Fundamentals of Physics. 9th Edition, Wiley, New York, 904-907.
[10]
Hecht, E. (2002) Optics. 4th Edition, Pearson Education, Delhi, 106-111.
