## MatLab Programs (Under Construction...)

 Description: This is a program writen by Luigi Giaccari which computes triangulations (by two simplices) of point cloud data in three-dimensions. Very useful for plotting two dimensional surfaces given by point data. Matlab Central Page Author's Page(Find other cool matlab programs here as well.)
 This first collection of programs are associated with the introduction note set for the N-Body problem. nBodyWpar.m: This is the main files needed for the simulation of the N-Body problem. This file codes the vector field for the problem as a matLab function. The number of bodies, as well as their masses and the gravitational constant must be passed along with the current position, to the function. nBodyPlayGround.m: A test program for the program 'nBodyWpar.m'. Before running this program set the number of bodies 'N', the gravitational constant 'G', and the length of the simulation 'simulationTime'. The program then generates random masses and initial conditions and integrates the resulting system. The output is several graphs illustrating the results. The program is fun to play with but also demonstrates that 'nBodyWpar.m' works properly with any number of bodies and parameter values that may occur in other work. NbodyOne.m:: The program is used in the introduction set of notes to look at the five body problem with symmetric initial conditions. It calls the program 'rstTOijk.m' to carry out some coordinate transformations described in those notes, and the program 'nBodyWpar.m' for the integration. rstTOijk.m: This function computes a coordinate transformation used in NbodyOne.m. twobodyDesign.m: The program is used in the introduction note set to design elliptic orbits in the two body problem with desired properties (eccentricity ect). sitnikovMap.m: The program simulates the Sitnikov problem (actually the continuation of the Sitnikov problem into the three body problem, but with very small perturbation parameter). It is used to produce the results in the introduction set of notes that pertain to the Sitnikov problem. The output is a couple of Poincare maps and plots of the height of the third body and the configuration of the entire system in physical space (R^3). The program lets the user define both the number of initial conditions to be included in the map, and the number of intersections of each trajectory with the Poincare section. NOTE: This program replaces the program 'sitnikov.m' which use to be posted here. That program had several errors and more importantly did not allow the number of crossings to be set at run time. One simpley integrated for 'a long time' and hoped to find enough. sitnikovNewton.m: This function is used in the program 'sitnikovMap.m'. The caller passes a pair of points, one on each side of the Poincare section where neither are with in the prescribed tolerence which would allow them to be considered intersections. The function implements a Newton algorithm which takes this as the 'initial guess' and then converges to a true intersection between them.
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