Electrophysiological Muscle ODE System (Q6674244)

One continuum mechanics three-dimensional model for each participant. The equations originate from conservation of mass and momentum for each participant.

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defining formula

{\begin{aligned}\rho _{{\text{M}}1}\mathbf {\ddot {x}} _{{\text{M}}1}&=\mathbf {\nabla } \cdot \left(\mathbf {P} _{\text{passive}}(\mathbf {F} _{{\text{M}}1})+\mathbf {P} _{\text{active}}(\mathbf {F} _{{\text{M}}1},\gamma _{{\text{M}}1})-p_{{\text{M}}1}\mathbf {F} _{{\text{M}}1}^{-T}\right),&\mathbf {\nabla } \cdot \ \mathbf {\dot {x}} _{{\text{M}}1}=0\ &{\text{in}}\ \Omega _{{\text{M}}1}\times [0,T_{\text{end}})\\\rho _{{\text{M}}2}\mathbf {\ddot {x}} _{{\text{M}}2}&=\mathbf {\nabla } \cdot \left(\mathbf {P} _{\text{passive}}(\mathbf {F} _{{\text{M}}2})+\mathbf {P} _{\text{active}}(\mathbf {F} _{{\text{M}}2},\gamma _{{\text{M}}2})-p_{{\text{M}}2}\mathbf {F} _{{\text{M}}2}^{-T}\right),&\nabla \cdot \ \mathbf {\dot {x}} _{{\text{M}}2}=0\ &{\text{in}}\ \Omega _{{\text{M}}2}\times [0,T_{\text{end}})\\\rho _{\text{T}}\mathbf {\ddot {x}} _{\text{T}}&=\mathbf {\nabla } \cdot \left(\mathbf {P} _{\text{passive}}(\mathbf {F} _{\text{T}})-p_{\text{T}}\mathbf {F} _{\text{T}}^{-T}\right),&\mathbf {\nabla } \cdot \ \mathbf {\dot {x}} _{\text{T}}=0\ &{\text{in}}\ \Omega _{\text{T}}\times [0,T_{\text{end}})\end{aligned}}

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mardi Formula:6674244