Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
Control of Calculations in the Beam Dynamics using Approximate Invariants. / Andrianov, S.; Zyuzin, D.
Control of Calculations in the Beam Dynamics using Approximate Invariants. 2014. p. 3041-3043.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
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TY - GEN
T1 - Control of Calculations in the Beam Dynamics using Approximate Invariants
AU - Andrianov, S.
AU - Zyuzin, D.
PY - 2014
Y1 - 2014
N2 - One of the important problems in the theory of dynamical systems is to find corresponding (invariants). In this article we are discussing some problems of computing of invariant functions (invariants) for dynamical systems. These invariants can be used for describing of particle beams systems. The suggested method is constructive and based on the matrix formalism for Lie algebraic tools. We discuss two types of invariants: kinematic and dynamic. All calculations can be realized in symbolic forms, in particular, kinematic invariants are based on the theory of representations of Lie algebras (in particular, using the Casimir’s operators). For the case of nonlinear kinematic invariants we propose a recursive scheme, which can be implemented in symbolic forms using instruments of computer algebra (for example, such packages as Maple or Mathematica). The corresponding expressions for invariants can be used to control the correctness of computational experiments, first of all for long time beam dynamics.
AB - One of the important problems in the theory of dynamical systems is to find corresponding (invariants). In this article we are discussing some problems of computing of invariant functions (invariants) for dynamical systems. These invariants can be used for describing of particle beams systems. The suggested method is constructive and based on the matrix formalism for Lie algebraic tools. We discuss two types of invariants: kinematic and dynamic. All calculations can be realized in symbolic forms, in particular, kinematic invariants are based on the theory of representations of Lie algebras (in particular, using the Casimir’s operators). For the case of nonlinear kinematic invariants we propose a recursive scheme, which can be implemented in symbolic forms using instruments of computer algebra (for example, such packages as Maple or Mathematica). The corresponding expressions for invariants can be used to control the correctness of computational experiments, first of all for long time beam dynamics.
M3 - Conference contribution
SN - 9783954501328
SP - 3041
EP - 3043
BT - Control of Calculations in the Beam Dynamics using Approximate Invariants
ER -
ID: 7028141