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)
“Writing a book I have found to be like building a house. A man forms a plan, and collects materials. He thinks he has enough to raise a large and stately edifice; but after he has arranged, compacted and polished, his work turns out to be a very small performance. The authour however like the builder, knows how much labour his work has cost him; and therefore estimates it at a higher rate than other people think it deserves,”
—James Boswell (1740–1795)
“What if all the forces of society were bent upon developing [poor] children? What if society’s business were making people instead of profits? How much of their creative beauty of spirit would remain unquenched through the years? How much of this responsiveness would follow them through life?”
—Mary Heaton Vorse (1874–1966)
“Between the acting of a dreadful thing
And the first motion, all the interim is
Like a phantasma or a hideous dream.
The genius and the mortal instruments
Are then in council, and the state of man,
Like to a little kingdom, suffers then
The nature of an insurrection.”
—William Shakespeare (1564–1616)
“The essence of statesmanship is not a rigid adherence to the past, but a prudent and probing concern for the future.”
—Hubert H. Humphrey (1911–1978)
“And yet we constantly reclaim some part of that primal spontaneity through the youngest among us, not only through their sorrow and anger but simply through everyday discoveries, life unwrapped. To see a child touch the piano keys for the first time, to watch a small body slice through the surface of the water in a clean dive, is to experience the shock, not of the new, but of the familiar revisited as though it were strange and wonderful.”
—Anna Quindlen (b. 1952)