0. Basic concepts of kinematics and dynamics of systems of particles and rigid bodies
1.Equations of motion of free particles and system of free particles in general
coordinates Lagrange equations of the second kind, a generalization forces, generalized
potential Lagrangian, conservative force, dissipative force.
2.Dynamics of bound particles and rigid bodies
The principle of relaxation, Lagrangian equations of the first kind, Lagrange equations
second kind for holonomic systems.
3.Differential mechanical principles
The principle of virtual work, reversible and irreversible shift, the equilibrium conditions
coupled mechanical systems.
D'Alembert's principle, the inertial force, d'Alembert principle of continuity
Lagrange equations of the first kind. Central Lagrange equation and its
write using the general momentum associated with Lagrange's equations
second kind. Differential variational principles: the principle of Gauss, Jourdainův
principle.
4.Integral mechanical principles
Hamilton's principle, Lagrange equations for invariance bodobých
transformations, first integrals Lagrange equations.
Maupertuisův principle Jacobi principle.
5.Canonical equations and transformation
Hamilton's equations, Hamilton's functions, Legendre transformation, derivation
canonical equations of Hamilton's principle, Poisson brackets.
Canonical transformations, invariants of canonical transformations. Hamilton-
Jacobi equation.
6.Rigid body
Kinematics of rotational motion of a rigid body: folding the final turn,
Euler angles, Euler kinematic equations. Dynamics of a rigid body:
equivalence system of forces acting on a rigid body, the center of the system
parallel forces, translational and rotational motion of a rigid body, tensor
inertia of a rigid body, Euler dynamic equations of rigid rotation
around a fixed point and a fixed axis, moving Lagrangian
rigid body.
1.Equations of motion of free particles and system of free particles in general
coordinates Lagrange equations of the second kind, a generalization forces, generalized
potential Lagrangian, conservative force, dissipative force.
2.Dynamics of bound particles and rigid bodies
The principle of relaxation, Lagrangian equations of the first kind, Lagrange equations
second kind for holonomic systems.
3.Differential mechanical principles
The principle of virtual work, reversible and irreversible shift, the equilibrium conditions
coupled mechanical systems.
D'Alembert's principle, the inertial force, d'Alembert principle of continuity
Lagrange equations of the first kind. Central Lagrange equation and its
write using the general momentum associated with Lagrange's equations
second kind. Differential variational principles: the principle of Gauss, Jourdainův
principle.
4.Integral mechanical principles
Hamilton's principle, Lagrange equations for invariance bodobých
transformations, first integrals Lagrange equations.
Maupertuisův principle Jacobi principle.
5.Canonical equations and transformation
Hamilton's equations, Hamilton's functions, Legendre transformation, derivation
canonical equations of Hamilton's principle, Poisson brackets.
Canonical transformations, invariants of canonical transformations. Hamilton-
Jacobi equation.
6.Rigid body
Kinematics of rotational motion of a rigid body: folding the final turn,
Euler angles, Euler kinematic equations. Dynamics of a rigid body:
equivalence system of forces acting on a rigid body, the center of the system
parallel forces, translational and rotational motion of a rigid body, tensor
inertia of a rigid body, Euler dynamic equations of rigid rotation
around a fixed point and a fixed axis, moving Lagrangian
rigid body.