https://github.com/krproject-tech/mbd_demo
Multi-Body Dynamics Closed-loop Pendulum demo
https://github.com/krproject-tech/mbd_demo
matlab multibody-dynamics phisics-engine
Last synced: 2 months ago
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Multi-Body Dynamics Closed-loop Pendulum demo
- Host: GitHub
- URL: https://github.com/krproject-tech/mbd_demo
- Owner: KRproject-tech
- License: mit
- Created: 2022-10-02T11:53:51.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2025-02-13T15:01:22.000Z (4 months ago)
- Last Synced: 2025-02-13T16:23:19.698Z (4 months ago)
- Topics: matlab, multibody-dynamics, phisics-engine
- Language: MATLAB
- Homepage:
- Size: 38.2 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
#
MBD_demo
**Communication**
**Language**
__Closed-loop Pendulum smaple code by 3D Multi-Body Dynamics__
## Overview
The Closed-loop Pendulum demo which is modeled by Quaternion based Multi-Body Dynamics.
The following dynamics for multi-bodies are solved [^2].
$$
\left[
\begin{array}{cccc}
{\bf M_G} & {\bf 0} & \partial_{{\bf r_G}} {\bf C}^T & {\bf 0} \\
{\bf 0} & 4{\bf L_G}^T {\bf J_G}' {\bf L_G} & \partial_{\bf \varepsilon} {\bf C}^T & \partial_{\bf \varepsilon} {\bf C}^T_E \\
\partial_{{\bf r_G}} {\bf C} & \partial_{\bf \varepsilon} {\bf C} & {\bf 0} & {\bf 0} \\
{\bf 0} & \partial_{\bf \varepsilon} {\bf C}_E & {\bf 0} & {\bf 0} \\
\end{array}
\right]
\left[
\begin{array}{c}
\ddot{\bf r}_G \\
\ddot{\bf \varepsilon} \\
{\bf \lambda} \\
{\bf \lambda}_E \\
\end{array}
\right]
=\left[
\begin{array}{c}
{\bf F}_G \\
8d_T {\bf L}^T_G {\bf J}'_G d_T {\bf L}_G {\bf \varepsilon} + 2 {\bf L}^T_G {\bf n}'_G \\
{\bf \gamma} \\
{\bf \gamma}_E \\
\end{array}
\right],
$$
where
$$
{\bf C} ({\bf r_G}, {\bf \varepsilon}) = {\bf 0},
$$
is the geometrical constraint condition, and
$$
{\bf C}_E ({\bf \varepsilon}) :=
\left[
\begin{array}{c}
{\bf \varepsilon}^T_1 {\bf \varepsilon}_1 - 1 \\
\vdots \\
{\bf \varepsilon}^T_N {\bf \varepsilon}_N - 1 \\
\end{array}
\right] = {\bf 0},
$$
is constraint condition for Euler parameter.
Baumgarte constraint stabilization method [^1] is employed to above Differential-algebraic system of equations (DAE).
## Preparation before analysis
Show procedures
__[Step 1] Install the ToolBoxes__
The following ToolBoxes in “./ ToolBoxes/” are required,
* “mmwrite” by Micah Richert:
https://jp.mathworks.com/matlabcentral/fileexchange/15881-mmwrite
__[Step 1.2] Add path to installed ToolBoxes__
Modify "add_pathes.m".
__[Step 2] Start GUI form__
Open the “GUI.fig” from MATLAB.
__[Step 2.1] Pre-setting__
Push the "Parameters" buttun and edit parameters.
__[Step 3] Start analysis__
Push the “exe” button and wait until the finish of the analysis.
__[Step 4] Plot results__
Push the “plot” button.
## Image
Time series of energy (conserved)
Error of constraint conditions
## Movie
https://user-images.githubusercontent.com/114337358/193452979-66b5f130-e993-44fa-aaef-a5bad153d087.mp4
Chaotic behevior is generated because the masses of the left and right rigid bodies are different.
### References
[^1]: J. Baumgarte，“Stabilization of Constraints and Integrals of Motion in Dynamical Systems”，Computer Methods in Applied Mechanics and Engineering，pp.1–16，1972.
[^2]: 日本機械学会編，マルチボディダイナミクス〈1〉基礎理論，コロナ社．