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

ConfigSpring – Linear Spring acting on a configuration variable

Unlike the LinearSpring which creates a spring force between two points in 3D space, a ConfigSpring implements a spring force directly on a generalized coordinate:

\[F_{q} = -k (q - q_0)\]

where \(k\) is the spring stiffness and \(q_0\) is the neutral “length” of the spring.

Implemented Calculations

Calculation	Implemented
V	Y
V_dq	Y
V_dqdq	Y
V_dqdqdq	Y

Examples

We can create a simple 1D harmonic oscillator using ConfigSpring on a translational configuration variable. The same oscillator could be created using a LinearSpring as well.

import trep
from trep import tx,ty,tz,rx,ry,rz

# Create a sytem with one mass that moves in the x direction.
system = trep.System()
system.import_frames([tx('x', mass=1, name='block')])

trep.potentials.ConfigSpring(system, 'x', k=20, q0=0)

A ConfigSpring can be used to create a torsional spring on a rotational configuration variable. Here we create a pendulum with a length of 2 and mass of 1. Instead of gravity, the pendulum is moved by a single torsional spring.

import trep
from trep import tx,ty,tz,rx,ry,rz

system = trep.System()
system.import_frames([
    ry("theta"), [
        tz(2, mass=1)
        ]])

trep.potentials.ConfigSpring(system, 'theta', k=20, q0=0.7)

ConfigSpring Objects

class trep.potentials.ConfigSpring(system, config, k[, q0=0.0, name=None])

Create a new spring acting on the specified configuration variable. The configuration variable must already exist in the system.

ConfigSpring.config

The configuration variable that spring depends and acts on.

(read only)

ConfigSpring.q0

The “neutral length” of the spring. When self.config.q == q0, the force is zero.

ConfigSpring.k

The spring constant of the spring.