- #1
Franky4
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Homework Statement
I was given a task to model (using Matlab) 3 identical particles in external field and find spectra of lowest system energy states using gradient descend method for each particle in the system.
I did a run of 500 random generated coordinates and found this distribution.
Now I need to find natural frequency and vectors for the lowest energy state system of 4.5299 units in this case. Also find eigen vectors for different nodes.
Homework Equations
Potential due to external field: U(x,y) = x^3 + x^4 - 0.1*x + y^6 - x*y;
Potential due to interactions between particles: U(r1, r2) = a/(abs(r1 - r2)); a is a constant.
The Attempt at a Solution
I found plenty of information for systems with masses, springs and stiffness coefficients, but nothing for this and I am not sure which way to proceed. Should I be trying to think of this three particle bound system as three masses (charges in this case) connected with different springs (coulomb force) for which stiffness k should be calculated from the force by the gradient of external field and repulsion force between particles or am I overthinking this.
First time posting, not sure between introductory and advanced homework sections