docs:utils:findsoln
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docs:utils:findsoln [2010/03/04 08:39] gibson |
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| * relative equilibrium: //σ = // a translation that scales linearly in //T//, all //T// (also called a traveling wave) | * relative equilibrium: //σ = // a translation that scales linearly in //T//, all //T// (also called a traveling wave) | ||
| * periodic orbit: //σ = 1// and some finite value of //T// (and integer multiples of it) | * periodic orbit: //σ = 1// and some finite value of //T// (and integer multiples of it) | ||
| - | * preperiodic orbit: //σ ≠ 1// but //σ^n = 1// for some //n>1//, and some finite value of //T// (and integer multiples_ | + | * preperiodic orbit: //σ ≠ 1// but //σ^n = 1// for some //n>1//, and some finite value of //T// (and integer multiples) |
| * relative periodic orbit: some element //σ// of the appropriate symmetry group, and some finite value of //T// (and integer multiples) | * relative periodic orbit: some element //σ// of the appropriate symmetry group, and some finite value of //T// (and integer multiples) | ||
| + | The preperiodic orbit is a portion of a periodic orbit, so I haven't really counted it as a separate solution type. | ||
| You specify which kind of solution to find with the <code> -eqb, -orb, -xrel, -zrel</code> options. The symmetry σ for the relative equilibrium and relative periodic orbit solutions involves unknown phase shifts (translations) in //x//, //z//, or both //x,z//, depending on the symmetry of the initial guess //u//, and you specify which to treat as unknowns by using the ''-xrel'' and ''-zrel'' options. Here are some examples of searches of various types | You specify which kind of solution to find with the <code> -eqb, -orb, -xrel, -zrel</code> options. The symmetry σ for the relative equilibrium and relative periodic orbit solutions involves unknown phase shifts (translations) in //x//, //z//, or both //x,z//, depending on the symmetry of the initial guess //u//, and you specify which to treat as unknowns by using the ''-xrel'' and ''-zrel'' options. Here are some examples of searches of various types | ||
docs/utils/findsoln.txt · Last modified: 2010/03/04 17:37 by gibson
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