gait journal latex math

latex_math.tex

#for equation 3
\begin{align*}
\alpha &= 
\begin{cases}
\tan^{-1}{\frac{|J_{2x}-J_{1x}|}{|J_{2y}-J_{1y}|}} & J_{2y} \neq J_{1y}\\
\pi/2 & J_{2y} = J_{1y}
\end{cases} \\ \noalign{\vskip10pt}

\beta &= 
\begin{cases}
\tan^{-1}{\frac{|J_{3x}-J_{1x}|}{|J_{3y}-J_{1y}|}} & J_{3y} \neq J_{1y}\\
\pi/2 & J_{3y} = J_{1y}
\end{cases} \\ \noalign{\vskip10pt}
\theta &= \alpha + \beta
\end{align*}



for equation 5
\triangle x^{t}_{1} =\frac{x^{t+1}_{1} - x^{t}_{1}}{\sum_{i=1}^{8}\parallel p^{t+1}_{i} - p^{t}_{i}\parallel_2} \\ \noalign{\vskip8pt}
\triangle y^{t}_{1}=\frac{y^{t+1}_{1} - y^{t}_{1}}{\sum_{i=1}^{8}\parallel p^{t+1}_{i} - p^{t}_{i}\parallel_2} \\ \noalign{\vskip8pt}
{\bf f}_{displacement} = [\triangle x_{1}, \triangle y_{1}, \triangle x_{2}, \triangle y_{2}..., \triangle x_{8}, \triangle y_{8}]^{T}




for equation 8
\begin{align*}
L_s &=-\sum_{i=1}^{m}log{\frac{e^{W_{y_i}^{T}x_i + b_{y_i}}}{\sum_{j=1}^{n}{e^{W_{j}^{T}x_i+ b_j}}}} \\  \noalign{\vskip10pt}
L_c &= \frac{1}{2}\sum_{i=1}^{m}{\parallel{{\boldsymbol x_i}-{\boldsymbol c_{y_i}}}\parallel}_2^2 \\   \noalign{\vskip10pt}
L &= L_s + \lambda L_c + \lambda_{\theta}\parallel{\theta}\parallel_{2}
\end{align*}



for equation 10
s = {\arg\max}_{i\in(1, 2, ...,n)}{\sum_{t=1}^{N}s_i^t}