Полная производная по времени от момента ускорения

Last modified by Alexey Popov on 2019/06/17 20:12

\mathbf m = \frac{D \mathbf r \times \mathbf a(t,\mathbf r(t))}{Dt} = \frac{\partial \mathbf r \times \mathbf a}{\partial t} + (\mathbf u \cdot \nabla)(\mathbf r \times \mathbf a )

где 

 \left(\mathbf {u} \cdot \nabla \right)(\mathbf r \times \mathbf {a}) =\frac{1}{2} \left ( \nabla \left((\mathbf r \times \mathbf {a}) \cdot \mathbf {u} \right)- (\mathbf r \times \mathbf {a}) \left(\nabla \cdot \mathbf {u} \right)\,+\,\mathbf {u} \left(\nabla \cdot (\mathbf r \times \mathbf {a}) \right) \,+\,\nabla \times \left((\mathbf r \times \mathbf {a}) \times \mathbf {u} \right)  - (\mathbf r \times \mathbf {a}) \times \left(\nabla \times \mathbf {u} \right)-\mathbf {u} \times \left(\nabla \times (\mathbf r \times \mathbf {a}) \right) \right)

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Created by Alexey Popov on 2019/06/17 20:12