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Formula:9955

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Digital Library of Mathematical Functions ID 32.6.E24

ζ ⁢ H III ⁢ ( q , p , ζ ) = q 2 ⁢ p 2 - ( η ∞ ⁢ q 2 + θ 0 ⁢ q - η 0 ⁢ ζ ) ⁢ p + 1 2 ⁢ η ∞ ⁢ ( θ 0 + θ ∞ ) ⁢ q , 𝜁 subscript H III 𝑞 𝑝 𝜁 superscript 𝑞 2 superscript 𝑝 2 subscript 𝜂 superscript 𝑞 2 subscript 𝜃 0 𝑞 subscript 𝜂 0 𝜁 𝑝 1 2 subscript 𝜂 subscript 𝜃 0 subscript 𝜃 𝑞 {\displaystyle{\displaystyle\zeta\mathrm{H}_{\mbox{\scriptsize III}}(q,p,\zeta% )=q^{2}p^{2}-\left(\eta_{\infty}q^{2}+\theta_{0}q-\eta_{0}\zeta\right)p+\tfrac% {1}{2}\eta_{\infty}(\theta_{0}+\theta_{\infty})q,}}


Constraint(s)

Symbols List

  • q 𝑞 {\displaystyle{\displaystyle q}} : coordinate
  • H ⁢ ( q , p , z ) H 𝑞 𝑝 𝑧 {\displaystyle{\displaystyle\mathrm{H}(q,p,z)}} : Hamiltonian
  • θ 𝜃 {\displaystyle{\displaystyle\theta}} : parameter
  • p 𝑝 {\displaystyle{\displaystyle p}} : momentum
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