Search results
Results from the WOW.Com Content Network
The fast marching method [1] is a numerical method created by James Sethian for solving boundary value problems of the Eikonal equation: | | = / () =Typically, such a problem describes the evolution of a closed surface as a function of time with speed in the normal direction at a point on the propagating surface.
Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows from solving [1] for
From the equation for uniform linear acceleration, the distance covered = + for initial speed =, constant acceleration (acceleration due to gravity without air resistance), and time elapsed , it follows that the distance is proportional to (in symbols, ), thus the distance from the starting point are consecutive squares for integer values of time elapsed.
The curve of fastest descent is not a straight or polygonal line (blue) but a cycloid (red).. In physics and mathematics, a brachistochrone curve (from Ancient Greek βράχιστος χρόνος (brákhistos khrónos) 'shortest time'), [1] or curve of fastest descent, is the one lying on the plane between a point A and a lower point B, where B is not directly below A, on which a bead slides ...
The Kepler problem and the simple harmonic oscillator problem are the two most fundamental problems in classical mechanics. They are the only two problems that have closed orbits for every possible set of initial conditions, i.e., return to their starting point with the same velocity (Bertrand's theorem). [1]: 92
Niels Henrik Abel attacked a generalized version of the tautochrone problem (Abel's mechanical problem), namely, given a function () that specifies the total time of descent for a given starting height, find an equation of the curve that yields this result.
The two-body problem in general relativity (or relativistic two-body problem) is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of light by gravity and the motion of a planet orbiting its sun
The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details