Here : http://jugend-forscht-sachsen.de/2012/teilnehmer/fachgebiet/id/5 http://jugend-forscht-sachsen.de/2012/teilnehmer/fachgebiet/... Analytical solution of

Here : http://jugend-forscht-sachsen.de/2012/teilnehmer/fachgebiet/id/5 http://jugend-forscht-sachsen.de/2012/teilnehmer/fachgebiet/... Analytical solution of two fundamental unsolved problems of particle dynamics Two problems in classical mechanics have withstood several centuries of mathematical endeavor. The first problem is therefore to calculate the trajectory of a body thrown at an angle in the Earth's gravitational field and Newtonian flow resistance. The underlying power law was discovered by Newton (17th century). The second problem is the objective description of a particle-wall collision under Hertzian collision force and linear damping. The collision energy was derived in 1858 by Hertz, a linear damping force has been known since Stokes (1850). This paper has so far only the analytical solution of this approximate or numerical targets for the problems solved. First, the two problems are solved fully analytically. For the first problem will be investigated further using the analytical solution, the physical behavior of the system and set up outline solutions for generalized models. For the second problem is carried out in order to increase efficiency and convergence control a semi-analytical optimization. Finally, the analytical results are compared with numerical solutions so as to validate accuracy and convergence to numerically.