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{\displaystyle \omega _{x'}^{2}+\omega _{y'}^{2}=\left(\cos \psi {\dot {\theta }}+\sin \psi \sin \theta {\dot {\phi }}\right)^{2}+\left(-\sin \psi {\dot {\theta }}+\cos...

{\vec {\omega }}=R_{3}(\psi )R_{2}(\theta )R_{1}(\phi )\left[{\begin{matrix}{\dot {\phi }}\\0\\0\end{matrix}}\right]+R_{3}(\psi )R_{2}(\theta...

{\vec {\omega }}=R_{1}(\psi )R_{2}(\theta )R_{3}(\phi )\left[{\begin{matrix}0\\0\\{\dot {\phi }}\end{matrix}}\right]+R_{1}(\psi )R_{2}(\theta...

ω t + ϕ i , {\displaystyle \Phi _{I}=\omega t+\phi _{i},}   and,    Φ V = ω t + ϕ v {\displaystyle \Phi _{V}=\omega t+\phi _{v}} . Note that P V {\displaystyle...

{\phi }}\\{\dot {\theta }}\\{\dot {\psi }}\end{matrix}}\right]=\left[{\begin{matrix}(\omega _{x}c_{\psi }-\omega _{y}s_{\psi })/c_{\theta }\\\omega _{x}s_{\psi...

  V i Φ j Ψ k Λ l {\displaystyle \Theta (V,\Phi ,\Psi ,\Lambda )=\sum _{i,j,k,l=1}^{3}\Theta _{i}^{\ jkl}\ V^{i}\Phi _{j}\Psi _{k}\Lambda _{l}} The reader...

{\hbar }{e}}\Delta \theta .}   Φ g = ∫ Ω ⋅ d S = ∫ ∇ × D ⋅ d S = ∮ L D ⋅ d l = ℏ m e Δ θ . {\displaystyle ~\Phi _{g}=\int \mathbf {\Omega } \cdot d\mathbf...

}{d\Omega }}=|f(k,\theta ,\phi )|^{2}} ∫ d Ω σ ( Ω ) = ∫ 0 2 π d ϕ ∫ 0 π sin ⁡ θ d θ | f ( θ , ϕ ) | 2 {\displaystyle \int d\Omega \,\sigma (\Omega )=\int...

thetadot=theta0*omega_n*np.cos(omega_n*t+phi) thetadotdot=-theta0*omega_n**2*np.sin(omega_n*t+phi) fig=plt.figure() ax=fig.add_subplot(311) plt.plot(t,theta,'bo-')...

t ) = i ℏ Φ ˙ ( t ) {\displaystyle -ex(t)f(t)E_{0}\sin(\omega t)\Phi (t)=i\hbar {\dot {\Phi }}(t)} . where the position operator becomes time dependent...

\theta ,t)=R(r)f(\theta )g(t)} in cylindrical coordinates, or z ( θ , ϕ , t ) = Y ( θ , ϕ ) g ( t ) . {\displaystyle z(\theta ,\phi ,t)=Y(\theta ,\phi...

{\displaystyle \theta _{f}=\theta _{0}+{\bar {\omega }}t=\theta _{0}+\omega _{0}t+{\tfrac {1}{2}}\alpha t^{2}\,.} ▭  ω f = ω 0 + α t . {\displaystyle \omega _{f}=\omega...

{\displaystyle \theta _{f}=\theta _{0}+{\bar {\omega }}t=\theta _{0}+\omega _{0}t+{\tfrac {1}{2}}\alpha t^{2}\,.} ▭  ω f = ω 0 + α t . {\displaystyle \omega _{f}=\omega...

{\Delta ^{2}-a^{2}\sin ^{2}\theta }{\rho ^{2}}}\right)dct^{2}+2{\frac {\omega }{c}}\varpi ^{2}dctd\phi -\varpi ^{2}d\phi ^{2}-{\frac {\rho ^{2}}{\Delta...

dA=r^{2}d\phi d\theta } A sphere = r 2 ∫ 0 π sin ⁡ θ d θ ∫ 0 2 π d ϕ = 4 π r 2 {\displaystyle A_{\text{sphere}}=r^{2}\int _{0}^{\pi }\sin \theta d\theta \int...

{r}}\sin \theta \cos \phi +r{\dot {\theta }}\cos \theta \cos \phi -r{\dot {\phi }}\sin \theta \sin \phi \\{\dot {r}}\sin \theta \sin \phi +r{\dot {\theta }}\cos...

\theta )~\cos \phi \\rv_{i}&={\cfrac {1}{\eta k^{2}}}\sum _{l=1}^{\infty }{\cfrac {i^{l-1}(2l+1)}{l(l+1)}}~\psi _{l}(kr)~P_{l}^{1}(\cos \theta )~\sin...

{\displaystyle \theta _{f}=\theta _{0}+{\bar {\omega }}t=\theta _{0}+\omega _{0}t+{\tfrac {1}{2}}\alpha t^{2}\,.} ▭  ω f = ω 0 + α t . {\displaystyle \omega _{f}=\omega...

&=\sin \theta \sin \phi |g\rangle +\cos \phi |e\rangle +\cos \theta \sin \phi |r\rangle \\|a^{0}\rangle &=\cos \theta |g\rangle -\sin \theta |r\rangle...

_{r}}}\rho d\rho d\phi dz_{d}}{{\hat {R}}_{p}+{\frac {\omega \rho x}{c}}\sin {\hat {\phi }}-{\frac {\omega \rho y}{c}}\cos {\hat {\phi }}}}.} where   μ...