Integration¶

Particula-beta Index / Particula Beta / Lagrangian / Integration

Auto-generated documentation for particula_beta.lagrangian.integration module.

leapfrog¶

Perform a single step of leapfrog integration on the position and velocity of a particle.

Leapfrog integration is a numerical method used for solving differential equations typically found in molecular dynamics and astrophysics. It is symplectic, hence conserves energy over long simulations, and is known for its simple implementation and stability over large time steps.

Arguments¶

position (Tensor): The current position of the particle.
velocity (Tensor): The current velocity of the particle.
force (Tensor): The current force acting on the particle.
mass (float): The mass of the particle.
time_step (float): The time step for the integration.

Returns¶

- tuple - Updated position and velocity of the particle after one time step.

Reference: - https://en.wikipedia.org/wiki/Leapfrog_integration

Signature¶

def leapfrog(
    position: torch.Tensor,
    velocity: torch.Tensor,
    force: torch.Tensor,
    mass: torch.Tensor,
    time_step: float,
) -> Tuple[torch.Tensor, torch.Tensor]: ...