$\newcommand{\deriv}[2][]{\dfrac{\partial #1}{\partial #2}} \newcommand{\tderiv}[2][]{\tfrac{\partial #1}{\partial #2}} \newcommand{\fderiv}[2][]{\dfrac{d #1}{d #2}} \newcommand{\derivII}[3][]{\dfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\tderivII}[3][]{\tfrac{\partial^2 #1}{\partial #2 \partial #3}} \newcommand{\derivIII}[4][]{\dfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\tderivIII}[4][]{\tfrac{\partial^3 #1}{\partial #2 \partial #3 \partial #4}} \newcommand{\derivIV}[5][]{\dfrac{\partial^4 #1}{\partial #2 \partial #3 \partial #4 \partial #5}} \newcommand{\half}{\tfrac{1}{2}} % Macro for 1/2 \newcommand{\ud}{\mathrm{d}} \newcommand{\op}{\circ} \newcommand{\dq}{\dot{q}} \newcommand{\ddq}{\ddot{q}} \newcommand{\dt}{\Delta t}$

LinearDamper – Linear damper between two points

LinearDamper creates a damping force between the origins of two coordinate frames in 3D space:

We can derive a mapping from the damper force to a force in the generalized coordinates by looking at the work done by the damper. The virtual work done by a damper is simply the damper force multiplied by the change in the damper’s length (distance):

\[ \begin{align}\begin{aligned}x = ||p_1 - p_2||\\f = -c \dot x\\F_{q_i} = f \deriv[x]{q_i}\end{aligned}\end{align} \]

where \(p_1\) and \(p_2\) are the origins of two coordinate frames and \(c\) is the damper coefficient.

Implemented Calculations

Calculation	Implemented
f	Y
f_dq	Y
f_ddq	Y
f_du	Y
f_dqdq	Y
f_ddqdq	Y
f_ddqddq	Y
f_dudq	Y
f_duddq	Y
f_dudu	Y

Examples

dual_pendulums.py

class trep.forces.LinearDamper(system, frame1, frame2, c[, name=None])

Create a new damper between frame1 and frame2. The frames must already exist in the system.

LinearDamper.frame1

The coordinate frame at one end of the damper.

(read only)

LinearDamper.frame1

The coordinate frame at the other end of the damper.

(read only)

LinearDamper.c

The damping coefficient of the damper.