Virtual Work of Forces Acting On A Rigid Body
An alternate formulation of rigid body dynamics that has a number of convenient features is obtained by considering the virtual work of forces acting on a rigid body.
The virtual work of forces acting at various points on a single rigid body can be calculated using the velocities of their point of application and the resultant force and torque. To see this, let the forces F1, F2 ... Fn act on the points R1, R2 ... Rn in a rigid body.
The trajectories of Ri, i=1,...,n are defined by the movement of the rigid body. The velocity of the points Ri along their trajectories are
where ω is the angular velocity vector of the body.
Read more about this topic: Rigid Body Dynamics
Famous quotes containing the words virtual, work, forces, acting, rigid and/or body:
“Neither dead nor alive, the hostage is suspended by an incalculable outcome. It is not his destiny that awaits for him, nor his own death, but anonymous chance, which can only seem to him something absolutely arbitrary.... He is in a state of radical emergency, of virtual extermination.”
—Jean Baudrillard (b. 1929)
“... anybody is as their land and air is. Anybody is as the sky is low or high, the air heavy or clear and anybody is as there is wind or no wind there. It is that which makes them and the arts they make and the work they do and the way they eat and the way they drink and the way they learn and everything.”
—Gertrude Stein (1874–1946)
“... we shall never become an immense power in the world until we concentrate all our money and editorial forces upon one great national daily newspaper, so we can sauce back our opponents every day in the year; once a month or once a week is not enough.”
—Susan B. Anthony (1820–1906)
“It would be easy ... to regard the whole of world 3 as timeless, as Plato suggested of his world of Forms or Ideas.... I propose a different view—one which, I have found, is surprisingly fruitful. I regard world 3 as being essentially the product of the human mind.... More precisely, I regard the world 3 of problems, theories, and critical arguments as one of the results of the evolution of human language, and as acting back on this evolution.”
—Karl Popper (1902–1994)
“Success makes men rigid and they tend to exalt stability over all the other virtues; tired of the effort of willing they become fanatics about conservatism.”
—Walter Lippmann (1889–1974)
“See an old unhappy bull,
Sick in soul and body both,
Slouching in the undergrowth
Of the forest beautiful,”
—Ralph Hodgson (c. 1871–1962)