Syllabus
Outlook
Mathematical models in physics
Displacement vector
Strain tensor
Tensor of finite strain. Physical meaning of the components of the tensor of finite strain. Principal axes of strain. Tensor of infinitesimal strain. Volume dilatation.
Stress vector and related problems
Body forces and surface forces. Stress vector. Conditions of equilibrium in integral form. Equations of motion in integral form.
Stress tensor
Components of the stress tensor. Cauchy’s formula. Conditions of equilibrium in differential form. Equations of motion in differential form.
Stress-strain relations
Rheological classifications of substances. Generalised Hooke’s law. Homogeneous strain. Relations among the elastic coefficients.
Equations of motion
Equation of motion for a homogeneous isotropic medium. Wave equations.
Foundations of hydrodynamics
The equations of motion in the Eulerian coordinates. Ideal fluid, equation of continuity, Bernoulli’s equation. Viscous fluid, the Navier-Stokes equation.
Annotation
Tensor of finite strain and tensor of infinitesimal strain. Stress tensor.
Equation of motion in integral and differential forms.
Generalised Hooke’s law. Hooke’s law for an isotropic medium.
Equation of motion for a homogeneous isotropic medium; wave equations. Foundations of hydrodynamics.