shoeboxpy 0.0.3

A shoebox approximation for a marine hydrodynamics model

shoeboxpy

Installation

pip install git+https://github.com/incebellipipo/shoeboxpy.git

Theory

The shoeboxpy package provides simulation models for vessels with 3 and 6 degrees of freedom (DOF). These models are based on rigid-body dynamics, including added mass, damping, Coriolis/centripetal effects, and restoring forces.

6-DOF Model

The 6-DOF model represents a rectangular "shoebox" vessel with the following states:

• Position and orientation in the inertial frame: $\eta = [x, y, z, \phi, \theta, \psi]$
• Velocities in the body frame: $\nu = [u, v, w, p, q, r]$

3-DOF Model

The 3-DOF model simplifies the dynamics to planar motion (surge, sway, yaw) with states:

• Position and orientation in the inertial frame: $\eta = [x, y, \psi]$
• Velocities in the body frame: $\nu = [u, v, r]$

Dynamics

Dynamics for both models are governed by:

$$ \begin{aligned} & \dot{\eta} = J(\eta)\nu\ & (M_{RB} + M_A)\dot{\nu} + (C_{RB}(\nu) + C_A(\nu))\nu + D\nu = \tau + \tau_{\mathrm{ext}} + g_{\mathrm{restoring}}(\eta) \end{aligned} $$

where:

• $M_{RB}$ and $M_A$ are the rigid-body and added mass matrices.
• $C_{RB}(\nu)$ and $C_A(\nu)$ are the Coriolis/centripetal matrices.
• $D$ is the linear damping matrix.
• $\tau$ and $\tau_{\mathrm{ext}}$ are control and external forces/moments.
• $g_{\mathrm{restoring}}(\eta)$ represents restoring forces in roll and pitch.

Both models use a 4th-order Runge-Kutta method for numerical integration, allowing for accurate simulation of vessel dynamics under various forces and moments.

Read the theory for more details.

Example

Here is an example of how to use the shoeboxpy package to simulate a 6-DOF vessel:

import numpy as np
from shoeboxpy.model6dof import Shoebox
from shoeboxpy.animate import animate_history

# Initialize the shoebox model
shoebox = Shoebox(
    L=1.0,  # Length (m)
    B=0.3,  # Width (m)
    T=0.03,  # Height (m)
    eta0=np.array([0.0, 0.0, 0.0, 0.1, 0.1, 0.1]),  # Initial position and orientation
    nu0=np.zeros(6),  # Initial velocities
    GM_phi=0.2,  # Metacentric height in roll
    GM_theta=0.2,  # Metacentric height in pitch
)

# Simulate for 10 seconds with a time step of 0.01 seconds
dt = 0.01
eta_history = []
for _ in range(int(10 / dt)):
    shoebox.step(tau=np.array([1.0, 0.2, 0.0, 0.0, 0.0, 0.1]), dt=dt)  # Apply control forces
    eta_history.append(shoebox.get_states()[0])  # Store position and orientation

# Convert history to a NumPy array for analysis or visualization
eta_history = np.array(eta_history)

animate_history(eta_history, dt=dt, L=1.0, B=0.3, T=0.2)  # Animate the results