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)
“A great world leader is gone. Liberty loving people around the globe are sad tonight. We are strengthened in the thought of President Roosevelt’s work for little people everywhere.”
—Lyndon Baines Johnson (1908–1973)
“And whoever forces himself to love anybody
begets a murderer in his own body.”
—D.H. (David Herbert)
“Often, when there is a conflict between parent and child, at its very hub is an expectation that the child should be acting differently. Sometimes these expectations run counter what is known about children’s growth. They stem from remembering oneself, but usually at a slightly older age.”
—Ellen Galinsky (20th century)
“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)
“It grieves me to think how far more profound and reverent a respect the law would have for literature if a body could only get drunk on it.”
—Mark Twain [Samuel Langhorne Clemens] (1835–1910)