Some generalisations of brachistochrone problem

摘要

300 years ago Johann Bernoulli solved the problem of brachistochrone (the problem of fining the fastest travel curve's form) using the optical Fer- mat concept. In the same way we solved some generalisations of this prob- lem. We obtained the fastest travel curve's form in a gravitational field for a point-like mass. When moving in a uniform gravitational field we considered the influence of the dry friction of drag.