class NormalForm

(Return to index)

Resonance-free normal form.

Find normal form of a truncated Taylor series map. Compute from representation of a map which can be a nil-potent, static or dynamic symplectic map. Implementation of an algorithm described in {CENTER} M. Berz, E. Forest and J. Irwin,{BR} Particle Accelerators, 1989, Vol. 24, pp. 91-107. {/CENTER}

Type:	Instantiable
Include file:	./Algebra/NormalForm.hh

Synopsis (including inherited members):

• Public members:
  • NormalForm (const VpsInvMap<double>&) ;
  • NormalForm () ;
  • NormalForm (const NormalForm&) ;
  • ~NormalForm () ;
  • int degreesOfFreedom ()const ;
  • const Tps<double>& normalForm ()const ;
  • const Tps<double>& normalisingMap ()const ;
  • const Vector<complex<double> >& eigenValues ()const ;
  • const Matrix<double>& eigenVectors ()const ;
  • Matrix<double> anharmonicity ()const ;
  • Tps<double> invariant (int)const ;
• Protected Members:
  • void orderModes (Vector<complex<double> >,Matrix<double>) ;

Documentation:

• Public members:

  NormalForm (const VpsInvMap<double>&) ;

  Constructor.
  Construct normal-form for map.

  Matrix<double> anharmonicity ()const ;

  Get anharmonicities.
  Return the anharmonicities as a symmetric matrix.

  int degreesOfFreedom ()const ;

  Get number of stable degrees of freedom.

  const Vector<complex<double> >& eigenValues ()const ;

  Get eigenvalues.
  Return the eigenvalues of the linear part as a complex vector.

  const Matrix<double>& eigenVectors ()const ;

  Get eigenvectors.
  Return the eigenvectors of the linear part in packed form.

  Tps<double> invariant (int)const ;

  Get invariant polynomial.
  Return the invariant polynomial for the mode i.

  const Tps<double>& normalForm ()const ;

  Get normal-form.
  Return normal-form map as a Lie transform.

  const Tps<double>& normalisingMap ()const ;

  Get normalising map.
  Return the normalising map as a Lie transform.

• Protected members: