Dynamics
Submodules
Drag in Granular Media
import pynamics from pynamics.frame import Frame from pynamics.variable_types import Differentiable,Constant from pynamics.
Go to Drag in Granular MediaOthers
Derivatives and the Golden Rule
$$ \frac{ {}^N{d\vec{v}}}{dt} = \frac{ {}^A{d\vec{v}}}{dt} + {}^N{\vec{w}}^{A} \times \vec{v} $$
Go to Derivatives and the Golden RuleDyads, Dyadics, and Inertia
Dyads Dyads and dyadics are a difficult concept to understand, initially.
Go to Dyads, Dyadics, and InertiaFalling Rod Example
This example shows how to implement contact and friction using a penalty method and damping
Go to Falling Rod ExampleForces and Torques
Introduction Non-Conservative Forces Damping $$\vec{f} = -b\vec{v}$$ Friction Friction is typically formulated as the forces acting between two bodies $A$ and $B$
Go to Forces and TorquesFour Bar Dynamics with unit Scaling
%matplotlib inline """ Written by Daniel M. Aukes Email: danaukes<at>gmail.com Please see LICENSE for full license.
Go to Four Bar Dynamics with unit ScalingFrames, Basis Vectors, and Vectors
Frames When analyzing a system, sometimes it’s convenient or simple to represent a system in a specific way.
Go to Frames, Basis Vectors, and VectorsInertias for common shapes
Rectangular parallelepiped/prism (a box) with length $a$, width $b$, height $c$
Go to Inertias for common shapesKane's method
Frames Frame A $$ {}^{N}{}{\vec{\omega}}^{A}{} = \dot{\theta} \hat{n}_z= \dot{\theta} \hat{a}_z $$
Go to Kane's methodRotations
Introduction While there may be many ways to navigate and describe the same three-dimensional space using reference frames, it is also necessary and desireable to be able to change representations; this can be useful for interpreting motion from a differet perspective, for adding forces or torques to a system using dirctional components which are a more natural description, or in order to perform mathematical operations between vectors which are represented by different basis vectors.
Go to RotationsTriple Pendulum Example
%matplotlib inline Try running with this variable set to true and to false and see the difference in the resulting equations of motion
Go to Triple Pendulum ExampleUnit Scaling
import idealab_tools.units idealab_tools.units.force kilogram*meter/second^2 idealab_tools.units.force.base_units {'kilogram': 1, 'meter': 1, 'second': -2} idealab_tools.
Go to Unit ScalingVariable Types
Variables in pynamics may be grouped into different categories, and used for different things.
Go to Variable TypesExternal Resources
References
- Kane, T. R., & Levinson, D. A. (1985). Dynamics: Theory and Applications, 402. https://doi.org/10.1016/0094-114X(86)90059-5
- Mitiguy, P. (2009). Advanced Dynamics and Motion Simulation.