The purpose of this lab is to become familiar with the classical dynamics of a system of point-like particles interacting via two-body forces.
Consider a system of N particles of a given mass (the same for all particles). The spherically-symmetrical two-body potential is of Lennard-Jones type:
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Write a program ljmd.f that integrates the Hamilton equations of motion for a number N (input parameter; consider up to 4 atoms) with a method which has an error of O(h5) per step.
Calculate and print at t=0 and after every 200 steps:
i. the total energy of the system;
ii. all components of the total linear momentum;
iii. all components of the center-of-mass (CM) of the system;
iv. all the components of the total angular momentum.
Calculate the following quantity at each time step:
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Write the results in a file an make a plot of it using gnuplot. You should use your own input file to test the program. I will use mine for grading. Your report should contain a short description of the problem (including equation of motion, numerical techniques, etc.) and a plot of the r.m.s. for your test input data.
You can use the FORTRAN program ~tomanek/PHY480/HW5/xrgkt4.f for the damped linear harmonic oscillator or an incomplete mock-up code ~tomanek/PHY480/HW5/ljmdmu.f as a template for your code ljmd.f. Your code should run with the input file ~tomanek/PHY480/HW5/Na3.xyz (or its obvious modifications for up to 4 particles) for a hypothetical Na3 atomic cluster. Use double precision in your calculations.