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Deformable Bodies Dynamics

A common problem that appears in engineering and mechanical systems consists of studying the possible motions of a given body in a controlled setting, such as in a lab, and then trying to understand what will be the body’s motion “in the wild”, such as when viewed from an inertial frame of reference. Examples where this happens are satellites self-adjusting in space or the complicated moves a cat does to right itself midair.

DeformableBodies.jl is a Julia package dedicated to aid in the construction and simulation of such problems. It allows the user to enter the body's motion as seem from an arbitrary frame of reference and calculates the motion from the perspective of an inertial frame.

The data needed for solving a deformable body problem consists of the body trajectory with respect to an arbitrary reference frame. Given this, we can reconstruct the body's trajectory from the point of view of an inertial frame as a sequence of rotations from one frame to the other. In order to avoid gimbal lock, all the rotations in this package are represented using unit quaternions.

Example

The figure below represents the movement that a falling cat1 does when righting itself midair both from the perspective of a frame rotating together with the cat and from an inertial frame.

Falling cat dynamics

Installation

This package can be installed using the Julia Package Manager. Simply open the REPL, enter ] and run

pkg> add DeformableBodies

Science behind the camera

This package is based on a scientific initiation that I did with Prof. Alejandro Cabrera while an undergraduate at UFRJ. Everything in here is based on Alejandro's paper:

  • Cabrera, Alejandro. “A Generalized Montgomery Phase Formula for Rotating Self-Deforming Bodies.” Journal of Geometry and Physics 57.5 (2007): 1405–1420. Crossref. Web.

Furthermore, this package strongly builds upon the fantastic work done by DifferentialEquations.jl and Plots.jl. Make sure to also check these projects.

Footnotes

  1. No real cats were harmed during the development of this program.