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:
“Tragedy dramatizes human life as potentiality and fulfillment. Its virtual future, or Destiny, is therefore quite different from that created in comedy. Comic Destiny is Fortune—what the world will bring, and the man will take or miss, encounter or escape; tragic Destiny is what the man brings, and the world will demand of him. That is his Fate.”
—Susanne K. Langer (1895–1985)
“We are weighed down, every moment, by the conception and the sensation of Time. And there are but two means of escaping and forgetting this nightmare: pleasure and work. Pleasure consumes us. Work strengthens us. Let us choose.”
—Charles Baudelaire (1821–1867)
“There is no longer beauty except in the struggle. No more masterpieces without an aggressive character. Poetry must be a violent assault against the unknown forces in order to overcome them and prostrate them before men.”
—Tommaso Marinetti (1876–1944)
“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)
“We are beginning a new era in our government. I cannot too strongly urge the necessity of a rigid economy and an inflexible determination not to enlarge the income beyond the real necessities of the government.”
—Andrew Jackson (1767–1845)
“Of all illusions in the world, the most universally received is the concern for reputation and glory, which we espouse even to the point of giving up riches, rest, life, and health, which are effectual and substantial goods, to follow that vain phantom and mere sound that has neither body nor substance.”
—Michel de Montaigne (1533–1592)