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Write a function that runs a n-body simulation of particles interacting via gravity only. The state vector `u` is a 2D array with dimensions N,6 of positions and velocities for each particle. Initial positions and velocities are provided in an initialization vector `uin` which is a 2D array with dimensions N,6 of positions and velocities. Particle masses are given by an array `mass` of size N containing the mass for each particle. Use the classical 4th order classical Runge-Kutta algorithm, integrating using a fixed step sized `dt` starting from `t0` and ending at `t1`.
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Write a function that runs a n-body simulation of N particles interacting via gravity only. The state vector `u` is a 2D array with dimensions N,6 of positions and velocities for each particle. Initial positions and velocities are provided in an initialization vector `uin` which is a 2D array with dimensions N,6 of positions and velocities. Particle masses are given by an array `mass` of size N containing the mass for each particle. Use the classical 4th order classical Runge-Kutta algorithm, integrating using a fixed step sized `dt` starting from `t0` and ending at `t1`.
Original LaTeX notation
Write a function that runs a n-body simulation of $N$ particles interacting via gravity only. The state vector `u` is a 2D array with dimensions N,6 of positions and velocities for each particle. Initial positions and velocities are provided in an initialization vector `uin` which is a 2D array with dimensions N,6 of positions and velocities. Particle masses are given by an array `mass` of size N containing the mass for each particle. Use the classical 4th order classical Runge-Kutta algorithm, integrating using a fixed step sized `dt` starting from `t0` and ending at `t1`.
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