Titlebook: Analytical Mechanics; A. I. Lurie Textbook 2002 Springer-Verlag Berlin Heidelberg 2002 Analytical Dynamics.Finite Rotation.Lagrangian Equa

敘述

Alle verschieden, alle gleich?,The kinetic energy of a system of particles is equal to half the sum of the masses multiplied by the velocities squared. We obtain an expression for the kinetic energy by replacing the generalised velocities v. with the expression given in eq. (1.3.3), i.e.

放肆的我

Antidiskriminierung versus Diskriminierung?,The sum of the elementary work due to the application of forces .. at points .. of a system undergoing virtual displacements .r. of these points from their positions at a fixed time instant is given by . The notation . is used to indicate that we are dealing with an infinitesimal quantity which is not a variation of the quantity ..

者變

人充滿活力

燒瓶

,Rigid body kinematics — basic knowledge,As mentioned in Chapter 1 rigid bodies and systems of rigid bodies are the most important objects of analytical mechanics. For this reason it is a worthwhile exercise to briefly review the basic formulae for rigid body kinematics and discuss some special problems in greater detail.

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Theory of finite rotations of rigid bodies,A rigid body having a fixed point . is subject to rotation through an angle . about an axis whose direction is given by unit vector e. The direction of e is chosen in such a way that watching from the end of vector e one observes the rotation through a positive angle ≤180°, that is counterclockwise for a right-handed coordinate system.

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Mnemonics

FID

palliative-care

Perturbation theory,Along with the given system of equations of motion . we consider an auxiliary (simplified) canonical system