Dynamics of Generalized Euler Tops with Constraints

نویسندگان

  • Dmitry V. Zenkov
  • Anthony M. Bloch
چکیده

We study the dynamics of the generalized Euler tops on various groups subject to left-invariant nonholonomic constraints. We blend together reconstruction and quasi-periodic Floquet theories to analyze the qualitative dynamics and discuss differences with the free rigid body motion. We also discuss some examples of particular interest.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Noncommutative extensions of elliptic integrable Euler-Arnold tops and Painleve VI equation

In this paper we suggest generalizations of elliptic integrable tops to matrix-valued variables. Our consideration is based on R-matrix description which provides Lax pairs in terms of quantum and classical R-matrices. First, we prove that for relativistic (and non-relativistic) tops such Lax pairs with spectral parameter follow from the associative Yang-Baxter equation and its degenerations. T...

متن کامل

Topics in Nonhamiltonian (magnetic{type) Interaction of Classical Hamiltonian Dynamical Systems. Ii. Generalized Euler{amp Ere Equations and Biot{savart Operators

The paper is devoted to the algebraico{analytic presentation of the Euler{Amp ere dynamical equations for two magnetically interacting massive systems (the charged Euler tops) and their generalizations. The interaction dynamics is based on the algebraic structure of isotopic pairs, which underlies the noncanonical version of Poisson brackets depending explicitely on the states of the acting sys...

متن کامل

Dynamics of the generalized Euler equations on Virasoro groups

We study the dynamics of the generalized Euler equations on Virasoro groups D̂(S1) with different Sobolev H metric (k ≥ 2) on the Virasoro algebra. We first prove that the solutions to generalized Euler equations will not blow up in finite time and then study the stability of the trivial solutions.

متن کامل

Approximation of a generalized Euler-Lagrange type additive mapping on Lie $C^{ast}$-algebras

Using fixed point method, we prove some new stability results for Lie $(alpha,beta,gamma)$-derivations and Lie $C^{ast}$-algebra homomorphisms on Lie $C^{ast}$-algebras associated with the Euler-Lagrange type additive functional equation begin{align*} sum^{n}_{j=1}f{bigg(-r_{j}x_{j}+sum_{1leq i leq n, ineq j}r_{i}x_{i}bigg)}+2sum^{n}_{i=1}r_{i}f(x_{i})=nf{bigg(sum^{n}_{i=1}r_{i}x_{i}bigg)} end{...

متن کامل

New Criteria for Existence of a Class of Generalized Euler-types Constants

One of the most important mathematical constants is Euler-Mascheroni constant that is the limit of the sequence --------------------------------  and is denoted by gamma. Some other developed constants known as Euler type constants are introduced in order to generalize the above constant. In the present paper, inspired by the functional sequence derivative of the limit summand of functions (i...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002