Equations, adjoint algebraic

Chapter 6 includes a priori estimates expressing stability of two-layer and three-layer schemes in terms of the initial data and the right-hand side of the corresponding equations. It is worth noting here that relevant elements of functional analysis and linear algebra, such as the operator norm, self-adjoint operator, operator inequality, and others are much involved in the theory of difference schemes. For the reader s convenience the necessary prerequisities for reading the book are available in Chapters 1-2. 

Claim 4.1.1 A field t described by the Euler equations of motion of a rigid body fixed in the centre of mass is tangent to the orbits 0 of the adjoint representation in the Lie algebra so(3) and is Hamiltonian on these orbits (which are homeomorphic to the spheres S ). 

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