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Energy and restrictions

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I'm trying to simulate a long chain of atoms where I restrict the bond (length between two consecutive atoms) and angle (between three consecutive atoms). Therefore, if I want to simulate N particles, then I have N+3 degrees of freedom. The only interactions between atoms is due to Lennard-Jones Potential.
I am using the classical Runge-Kutta fourth order method to integrate the equations. But, I got that the energy is always decreasing and then it keeps constant, like in the picture shown below.



What can I do to keep constant the energy ?

What is happening ? I'm new with the topic. My english is not that good, so if you do not understand something, just let me know it.
Thanks !

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