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Structure of the code

Project Structure

The structure of the code is as follows,

.
├── hdynamics
│   ├── hdynamics.py
|   ├── dynamics
|          ├── nbody.py
|          ├── harmonic_oscillator.py

The hdynamics.py file contains the base class for dynamical systems, which defines the interface and some common functionality, including methods to solve the Hamiltonian equations of motion. The dynamics directory contains specific implementations of dynamical systems, such as the harmonic oscillator and N-body systems, which we will study as examples.

We will discuss the individual components in the sections to come.

How these components work together?

By organising the code in this way, we can put many features that are common to all dynamical systems in the base class in hdynamics.py, allowing them to be reused in the specific implementations in the dynamics directory. This means we can easily add new dynamical systems by creating new files in the dynamics directory that inherit from the base class in hdynamics.py. Each specific dynamical system can then implement its own Hamiltonian and any other system-specific functionality while still benefiting from the common features provided by the base class.

The Dynamics Class

The Dynamics class is defined in hdynamics/hdynamics.py and serves as the base class for all dynamical systems. It provides a common interface and some shared functionality for all dynamical systems, including methods to solve the Hamiltonian equations of motion. The key methods in the Dynamics class are:

  • Constructor (__init__): Initializes the dynamics system with a specified number of dimensions. This is used to define the phase space of the system. Also creates a function jac_h which calculates the Jacobian of the Hamiltonian and stores it in the object.
  • H: This is the Hamiltonian of a dynamical system, and has to be specified for any dynamical system that is being implemented. This method is abstract, meaning it must be defined in any subclass that defines a dynamics system.
  • symplectic_form: Returns the symplectic form of the state of the system, which is used to compute the equations of motion. *rate_of_change: Returns a function that computes the rate of change of the state of the system, given the Hamiltonian. This is in a format suitable for use in an ODE solver.
  • generate_trajectory: Generates a trajectory of the system given an initial state, number of time steps and a length of timestep. This uses the function returned by the rate_of_change method to compute the evolution of the system over time.
  • plot_trajectory: Plots the trajectory of the system. This may be overridden in subclasses to define a way of plotting the trajectory that makes sense for that particular system.