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Display information for equation id:math.1989.31 on revision:1989

* Page found: Hamilton-Jacobische Differenzialgleichung (eq math.1989.31)

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TeX (original user input): 

S(q,\alpha ,t)=m\omega \int{dq}\sqrt{\left( \frac{2\alpha }{m{{\omega }^{2}}}-{{q}^{2}} \right)}-\alpha t=-\alpha t+m\omega \left[ \frac{q}{2}\sqrt{\left( \frac{2\alpha }{m{{\omega }^{2}}}-{{q}^{2}} \right)}+\frac{\alpha }{m{{\omega }^{2}}}\arcsin \left( q\sqrt{\frac{m{{\omega }^{2}}}{2\left| \alpha  \right|}} \right) \right]

TeX (checked): 

S(q,\alpha ,t)=m\omega \int {dq}{\sqrt {\left({\frac {2\alpha }{m{{\omega }^{2}}}}-{{q}^{2}}\right)}}-\alpha t=-\alpha t+m\omega \left[{\frac {q}{2}}{\sqrt {\left({\frac {2\alpha }{m{{\omega }^{2}}}}-{{q}^{2}}\right)}}+{\frac {\alpha }{m{{\omega }^{2}}}}\arcsin \left(q{\sqrt {\frac {m{{\omega }^{2}}}{2\left|\alpha \right|}}}\right)\right]

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MathML (25.296 KB / 3.094 KB) :

S ⁢ ( q , α , t ) = m ⁢ ω ⁢ ∫ 𝑑 q ⁢ ( 2 ⁢ α m ⁢ ω 2 - q 2 ) - α ⁢ t = - α ⁢ t + m ⁢ ω ⁢ [ q 2 ⁢ ( 2 ⁢ α m ⁢ ω 2 - q 2 ) + α m ⁢ ω 2 ⁢ arcsin ⁡ ( q ⁢ m ⁢ ω 2 2 ⁢ | α | ) ] 𝑆 𝑞 𝛼 𝑡 𝑚 𝜔 differential-d 𝑞 2 𝛼 𝑚 superscript 𝜔 2 superscript 𝑞 2 𝛼 𝑡 𝛼 𝑡 𝑚 𝜔 delimited-[] 𝑞 2 2 𝛼 𝑚 superscript 𝜔 2 superscript 𝑞 2 𝛼 𝑚 superscript 𝜔 2 𝑞 𝑚 superscript 𝜔 2 2 𝛼 {\displaystyle{\displaystyle S(q,\alpha,t)=m\omega\int{dq}\sqrt{\left(\frac{2% \alpha}{m{{\omega}^{2}}}-{{q}^{2}}\right)}-\alpha t=-\alpha t+m\omega\left[% \frac{q}{2}\sqrt{\left(\frac{2\alpha}{m{{\omega}^{2}}}-{{q}^{2}}\right)}+\frac% {\alpha}{m{{\omega}^{2}}}\arcsin\left(q\sqrt{\frac{m{{\omega}^{2}}}{2\left|% \alpha\right|}}\right)\right]}}

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MathML (2.772 KB / 436 B) :

S(q,α,t)=mω∫dq(2αmω2−q2)−αt=−αt+mω[q2(2αmω2−q2)+αmω2arcsin⁡(qmω22|α|)]

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