Dynamical similarity

Sloan, David James Austin (2018) Dynamical similarity. Physical Review D, 97: 123541. ISSN 1550-7998

[thumbnail of DynSimA2col]
PDF (DynSimA2col)
DynSimA2col.pdf - Accepted Version
Available under License Creative Commons Attribution-NonCommercial.

Download (306kB)


We examine “dynamical similarities” in the Lagrangian framework. These are symmetries of an intrinsically determined physical system under which observables remain unaffected, but the extraneous information is changed. We establish three central results in this context: (i) Given a system with such a symmetry there exists a system of invariants which form a subalgebra of phase space, whose evolution is autonomous; (ii) this subalgebra of autonomous observables evolves as a contact system, in which the frictionlike term describes evolution along the direction of similarity; (iii) the contact Hamiltonian and one-form are invariants, and reproduce the dynamics of the invariants. As the subalgebra of invariants is smaller than phase space, dynamics is determined only in terms of this smaller space. We show how to obtain the contact system from the symplectic system, and the embedding which inverts the process. These results are then illustrated in the case of homogeneous Lagrangians, including flat cosmologies minimally coupled to matter; the n-body problem and homogeneous, anisotropic cosmology.

Item Type:
Journal Article
Journal or Publication Title:
Physical Review D
Additional Information:
© 2018 American Physical Society
ID Code:
Deposited By:
Deposited On:
19 Mar 2019 15:30
Last Modified:
31 Dec 2023 01:03