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# TMN1

**Course:** Fundamentals of Mechanics

**Department/Abbreviation:** KEF/TMN1

**Year:** 2020

**Guarantee:** 'Mgr. Lukáš Richterek, Ph.D.'

**Annotation:** Introduction to the study of theoretical physics, Lagrange formalism of mechanics, Mechanics of a solid body, Hamilton formalism of mechanics. Introduction to mechanics of continuum.

**Course review:**

- Introduction to the study of theoretical physics, mechanics of a particles and particle system, components of velocity and acceleration, velocity and acceleration in curvilinear coordinates, dynamics of a particle, Newton Laws, particular problem from dynamics of a particle, system of particles, d'Alembert principle and equations of motion of a particle system, centre of mass of a system, classical integrals of motion, motion of a particle with variable mass
- Lagrange formalism of mechanics, systems subjected to bonds, classification of bonds, principle of virtual work and it applications, d'Alembert-Lagrange principle, Lagrange equations of the first kind and the second kind and their solutions for some particular situations, small oscillations of mechanical systems
- Mechanics of a solid body, basic terms from kinematics of a solid body, translation and rotation of a solid body, tensor of inertia and moments of inertia, Euler equations, motion of flywheels, motions in rotating systems
- Hamilton formalism of mechanics, Hamilton principle, Hamilton canonic equations, canonic transformations and their invariants, laws of conservation
- Introduction to mechanics of continuum, tensor of stress, volume and surface forces, vector of stress, equation of equilibrium of continuum, equations of motion of continuum, vector of displacement and tensor of deformation, generalized Hook Law, equation of equilibrium of an isotropic elastic body, equations of motion of an isotropic elastic body, oscillations and waves in an elastic body, vibration of elastic bodies, equation of a string
- Basics of mechanics of fluids, statics of fluids, equations of motion of an ideal fluid and their integrals, irrotational (steady) flow, motion of a viscous fluid, Navier-Stokes equation and theory of similarity