Systems#

class classes.System.SpringPendulumPolar#: Spherical pendulum in minimal coordinates (two angles).

class classes.System.RigidBodyMoving#

A rigid body moving through space. Makes use of director formulation, e.g. described in [1,2]. Only internal constraints. Subject to initial velocities and external acceleration.

References:

[1]: Betsch, P. and Steinmann, P. Constrained integration of rigid body dynamics. In: Computer Methods in Applied Mechanics and Engineering, 191(3-5): 467–488, 2001. doi: 10.1016/S0045-7825(01)00283-3.

[2]: Krenk, S. and Nielsen, M. B. Conservative rigid body dynamics by convected base vectors with implicit constraints. In: Computer Methods in Applied Mechanics and Engineering, 269: 437–453, 2014. doi: 10.1016/j.cma.2013.10.028.

class classes.System.DoublePendulum#: A double-pendulum: two point masses constrained by rigid bars. Length of the bars are determined from initial configuration.

class classes.System.DoubleFourBarLinkage#

A system consisting of 5 bars. Makes use of 2D director formulation, e.g. described in [1]. Internal constraints plus a constraint which fixes the top to the floor. Subject to initial velocities and external acceleration. More details can be found in [2].

References:

[1]: Betsch, P. and Uhlar, S.: Energy-momentum conserving integration of multibody dynamics, In: Multibody Syst Dyn, 17: 243–289, 2007. doi: 10.1007/s11044-007-9043-9.

[2]: Ivo Roupa, Sérgio B. Gonçalves, Miguel Tavares da Silva: Kinematics and dynamics of planar multibody systems with fully Cartesian coordinates and a generic rigid body, In: Mechanism and Machine Theory, 180: 105134, 2023, doi: 10.1016/j.mechmachtheory.2022.105134 .

class classes.System.FourParticleSystem#

Four masses, two of them connected via rigid bars (yields constraints), the other two with elastic springs (yields internal potential).

Lengths of the bars and resting length of the springs determined from initial configuration.

Inspired by: Gonzalez, O. Mechanical systems subject to holonomic constraints: Differential–algebraic formulations and conservative integration. In: Physica D: Nonlinear Phenomena, 132(1-2): 165–174, 1999. doi: 10.1016/S0167-2789(99)00054-8.

class classes.System.PendulumMinCoord#: Spherical pendulum in minimal coordinates (two angles).

class classes.System.HeavyTop#

A rigid gyroscopic top. Makes use of director formulation, e.g. described in [1,2]. Internal constraints plus a constraint which fixes the top to the floor. Subject to initial velocities and external acceleration.

References:

class classes.System.LagrangeTop#: A rigid gyroscopic top. Uses d_3 director and angular momentum as variables. See Bobenko & Suris (1996).

class classes.System.System#

Abstract system class. Contains all system described parameters

Property Summary

DIM#: spatial dimensions

DISS_MAT#: dissipation matrix

EXT_ACC#: external acceleration vector

GEOM#: vector with geometry parameters

MASS#: total mass (for multiple bodies vectorvalued)

MASS_MAT#: mass matrix

hasQuadraticConstraints#: specifies if all constraints are at most quadratic in the position

isCyclicCoordinate#: vector with boolean entries which are 1 for cyclic coordinates

mCONSTRAINTS#: total amount of scalar constraints

mMixedQuantities#: number of mixed quantities for integrator (e.g. strain)

nBODIES#: number of individual bodies

nConstraintInvariants#: number of invariants of the constraint on position level

nDOF#: total amount of degrees of freedom

nKineticInvariants#: number of invariants of the kinetic energy

nLM#: number of Lagrange multipliers

nPotentialInvariants#: number of invariants of the potential

nVconstraintInvariants#: number of invariants of the constraint on velocity level

class classes.System.SpringPendulum#: Spring pendulum with nonlinear elastic spring law.

class classes.System.RedundantTwoMassSpringSystem#: Two masses, connected via elastic springs (yields internal potential). Resting lengths of the springs determined from initial configuration.

class classes.System.TwoMassSpringSystem#: Two masses, connected via elastic springs (yields internal potential). Resting lengths of the springs determined from initial configuration.

class classes.System.Pendulum#: A simple pendulum: point mass constrained by a rigid bar to the origin. Length of the rod is determined from initial configuration.