Euler-Poincaré reduction  for systems with configuration space isotropy

Lawson, Jeffrey K.; Schmah, Tanya; Stoica, Cristina

doi:10.3934/jgm.2011.3.261

Cited by 1 publication

(3 citation statements)

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“…The stability of linear RE is determined using the theoretical findings in [Roberts & al. (2006)] and [Lawson & al. (2011)]) that we briefly present below.…”

Section: The Symplectic Slice Methods For Linear Rementioning

confidence: 99%

“…In the present stability calculations we employ two methods: for the isosceles RE, we use the splitting of the phase space of the REM method (see [Marsden (1992)]), whereas for the linear RE we introduce the Symplectic Slice method, that is a method with theoretical justification in [Roberts & al. (2006)] (also, see [Lawson & al. (2011)]).…”

Section: Stabilitymentioning

confidence: 99%

“…In this case we introduce the Symplectic Slice method, based on the theoretical work in [Roberts & al. (2006)] (but also see [Lawson & al. (2011)]).…”

Section: Introductionmentioning

confidence: 99%

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Notes on relative equilibria of isosceles molecules in classical approximation

McKinley

Paşca

Stoica

2019

Journal of Mathematical Physics

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We study a classical model of isosceles triatomic "A-B-A" molecules. The atoms, considered mass points, interact mutually via a generic repulsive-attractive binary potential. First we show that the steady states, or relative equilibria (RE), corresponding to rotations about the molecule symmetry axis may be determined qualitatively assuming the knowledge of 1) the shape of the binary interaction potential, 2) the equilibrium diatomic distances (i.e., the equilibrium bond length) of the A-A and A-B molecules, and 3) the distance at which the RE of the diatomic A-A molecule ceases to exist. No analytic expression for the interaction potentials is needed. Second we determine the stability of the isosceles RE modulo rotations using geometric mechanics methods and using Lennard-Jones diatomic potentials. As a by-product, we verify the qualitative results on RE existence and bifurcation. For isosceles RE we employ the Reduced Energy-Momentum method presented in [J.E. Marsden, Lectures in Mechanics, Cambridge University Press, 1992], whereas for linear (trivial isosceles) RE we introduce the Symplectic Slice method, a technique based on the findings in the paper [R.M. Roberts, T. Schmah and C. Stoica, Relative equilibria for systems with configurations space isotropy,

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“…The stability of linear RE is determined using the theoretical findings in [Roberts & al. (2006)] and [Lawson & al. (2011)]) that we briefly present below.…”

Section: The Symplectic Slice Methods For Linear Rementioning

confidence: 99%

Section: Stabilitymentioning

confidence: 99%