Learning Outcomes
1.The student can find a covariant or a contavariant vector or a tensor or the metric tensor.
2. The student knows what a continuous medium is whether it is in solid state or it a fluid (liquid or gas).
3. The student learns the motion of a contnuous medium, the velocity field and the notion of the trajectory of a particle.
4. The student learns the deformation tensor.
5. The student learns the stess tensor and the shear stress.
6. The student learns the continuity equation anthe equations of Euler for the motion of the continuous medium.
Course Content (Syllabus)
Curvilinear coordinate systems. natural and inverse natural basis. Covariant and contravariant vectrors and tensors. Metric tensor. Continuous media. Euler and Lagange variables. Accelaration of a particle. Deformation tensor. Geometric aspect of the deformation tensor. Evaluation of the deformation tensor from the translation vector. Main directions of the deformation tensor. Flow lines and trajectories of particles. Circulation of the velocity. Typical velocity fields and flows.
Continuity equation. The stress vector. The stress tensor. The Euler equations of motion. Balance of the momentum. Balance of the angular momentum. Main elements of the stess tensor. Maximum shear stress. Equilibrium condititions.