Chapter 3: Dynamics of Mechanical Systems Flashcards
Discuss the rigidity constraint.
The overall inertia forces and moments, as well as the overall kinetic energy of the body, result from an integration over the volume of the body, which is formally well-defined but practically of little use, since to be performed it requires the knowledge of the kinetmatic field inside the body: velocity, acceleration, etc. Since all bodies are deformable, their kinematic field depends on the solution of the dynamical problem.
In the case under assumption, we introduce an important assumption, that of the rigidity of the body. Such assumption qualifies as an idealization, a simplification and an approximation
1) Idealization
We idealize the notion that when a body is subjected to large motion but small deformation, the overall motion may dominate the dynamic loads the body is subjected to, depending on the rapidity of the motion
2) Simplification
3) Approximation
It neglects relevant aspects of the actual behavior of the system under evaluation; as such, to be acceptable the approximation must be justifiable and quantifiable.
Discuss the dynamics of a system of rigid bodies
When considering a system of rigid bodies, one needs to write the equations of motion of each body, which may include the forces and moments exchanged.
The exhchange of forces and moments according to the thirds of Newton’s principia, implies that any action (force or moment) body i exerts on body j, an analogoys action equal in magnitude but opposite in direction is exerted by body j on body i. Such actions are termed internal, in the sense that they act internally between members of the system.
Each of the equations of motion of each single body can be replaced by a suitable linear combinatin of equations of motion of bodies, provided none of the resulting equation is a linear combination of the others.
Combining the eqs of motion of different bodies may be especially useful when in the resulting equation some internal forces vanish.
