linear theory of equilibria
; this is SHM, which has small bounded trigonometric solutions, and so θ = 0 is a stable equilibrium. For θ = π + ε, that is, small perturbations about the upward vertical, we have
which has unbounded exponential solutions, and so θ = π is an unstable equilibrium.
Linearizing about (0,0,0), the three equations governing the Lorenz attractor give
where α,β,γ > 0. So r(t) = (x(t), y(t),z(t))T satisfies
If the matrix has distinct real eigenvalues λ1,λ2,λ3 with eigenvectors v1,v2,v3, then the solution is
This is a small bounded solution if λ1,λ2,λ3 are all negative; so the origin is stable when β<1.
- symmetric relation
- symmetry
- symmetry group
- symplectic geometry
- symplectic group
- synthetic geometry
- systematic error
- systematic sampling
- system of particles
- systems analysis
- Système International d'Unités
- Szemerédi's theorem
- T
- T
- T
- tableau
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- tacnode
- tail
- tangent
- tangent
- tangent bundle
- tangent field
- tangential
- tangent plane