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)
“I am not describing a distant utopia, but the kind of education which must be the great urgent work of our time. By the end of this decade, unless the work is well along, our opportunity will have slipped by.”
—Lyndon Baines Johnson (1908–1973)
“One never gets to know a person’s character better than by watching his behavior during decisive moments.... It is always only danger which forces the most deeply hidden strengths and abilities of a human being to come forth.”
—Stefan Zweig (18811942)
“It especially helps if you know that we’re all faking our adulthood—even your parents and their parents. Beneath these adult trappings—in our president, in our parents, in you and me—lurk the emotions of a child. If we know that only about ourselves, we become infantile; if we understand that about everybody, then we have nothing to be ashamed of—unless, of course, we go around acting like a child and expecting everyone else to act like grownups.”
—Frank Pittman (20th century)
“Pain hardens, and great pain hardens greatly, whatever the comforters say, and suffering does not ennoble, though it may occasionally lend a certain rigid dignity of manner to the suffering frame.”
—A.S. (Antonia Susan)
“Unlike femininity, relaxed masculinity is at bottom empty, a limp nullity. While the female body is full of internal potentiality, the male is internally barren.... Manhood at the most basic level can be validated and expressed only in action.”
—George Gilder (b. 1939)