Each chapter culminates with a classic scientific problem such as the brachistochrone
problem, the Einstein formula, NewtonAEs law of gravitation, the wave equation of the vibrating string, and HamiltonAEs principle.
The historic Brachistochrone problem consists of finding the shape of the curve along which a particle will descend, under gravity, from a point to another not directly below it, in the shortest amont of time.
DYNAMICAL QUANTITIES IN THE BRACHISTOCHRONE PROBLEM.
The historic Brachistochrone problem is widely discussed in the literature.
The calculus of variations is generally regarded as originating with the papers of Jean Bernoulli on the problem of the brachistochrone
Szarkowicz in 1995 , where the Monte Carlo method (an algorithm with the same principle as ES) is used to find an approximation to the classical brachistochrone problem.
In this work we are interested in two classical problems of the calculus of variations: the 1696 brachistochrone problem and the 1687 Newton's aerodynamical problem of minimal resistance (see, e.
Week 5: Derivation of the Nonlinear Differential Equation governing the Brachistochrone (Curve for which a ball travels from one point to another in the fastest time under the influence only of gravity), Solution to the Nonlinear Ordinary Differential Equation (Parametric Equations)
Physical Experiment 2: Timing a trajectory: the Brachistochrone vs.
The closest conventional analogue I could derive for this figure was a cycloid, L'Hospital's solution to Bernoulli's famous brachistochrone
problem, the curve traced by a fixed point on the circumference of a circle rolling along a straight line.