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)
“To fight oppression, and to work as best we can for a sane organization of society, we do not have to abandon the state of mind of freedom. If we do that we are letting the same thuggery in by the back door that we are fighting off in front of the house.”
—John Dos Passos (1896–1970)
“Her wrongs are ... indissolubly linked with all undefended woe, all helpless suffering, and the plenitude of her “rights” will mean the final triumph of all right over might, the supremacy of the moral forces of reason and justice and love in the government of the nation. God hasten the day.”
—Anna Julia Cooper (1859–1964)
“We are always acting on what has just finished happening. It happened at least 1/30th of a second ago. We think we’re in the present, but we aren’t. The present we know is only a movie of the past.”
—Tom Wolfe (b. 1931)
“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)
“When a natural king becomes a titular king, every body is pleased and satisfied.”
—Ralph Waldo Emerson (1803–1882)