How is geometry used in mechanics?
Geometric mechanics applies principally to systems for which the configuration space is a Lie group, or a group of diffeomorphisms, or more generally where some aspect of the configuration space has this group structure..
What are the dynamics of the systems of rigid bodies?
The dynamics of the rigid body consists of the study of the effects of external forces and couples on the variation of its six degrees of freedom.
The trajectory of any point in the body, used as reference point, gives the variation of three of these degrees of freedom..
What are the formulas used in the dynamics of rigid bodies?
For a rigid body, the angular momentum (L) is the product of the moment of inertia and the angular velocity: L = Iω.
For a point of mass, angular momentum can be expressed as the product of linear momentum and the radius ( r): L = mvr..
What is an example of a rigid body in mechanics?
A ball bearing made of hardened steel is an example of a rigid body.
A ball bearing loses almost no mechanical energy and retains its maximum shape upon bouncing or tapping.
Thus, it is an example of a rigid body..
What is mechanics of rigid bodies?
A branch of mechanics concerned with objects that are assumed to be perfectly rigid.
Rigid-body mechanics is used to describe and explain gross movements of humans and implements in sport and exercise.
It is subdivided into statics and dynamics..
What is the formula for the mechanics of rigid bodies?
The dynamics of rigid bodies rotating about fixed axes may be summarized in three equations.
The angular momentum is L = Iω, the torque is τ = Iα, and the kinetic energy is K = 1/2 Iω 2..
Why do we need to study dynamics of rigid bodies?
Rigid body mechanics is used extensively to design power generation and transmission systems, from jet engines, to the internal combustion engine, to gearboxes.
A typical problem is to convert rotational motion to linear motion, and vice-versa..
- For a rigid body, the angular momentum (L) is the product of the moment of inertia and the angular velocity: L = Iω.
For a point of mass, angular momentum can be expressed as the product of linear momentum and the radius ( r): L = mvr. - Geometric mechanics applies principally to systems for which the configuration space is a Lie group, or a group of diffeomorphisms, or more generally where some aspect of the configuration space has this group structure.
- Rigid body mechanics is used extensively to design power generation and transmission systems, from jet engines, to the internal combustion engine, to gearboxes.
A typical problem is to convert rotational motion to linear motion, and vice-versa. - The dynamics of the rigid body consists of the study of the effects of external forces and couples on the variation of its six degrees of freedom.
The trajectory of any point in the body, used as reference point, gives the variation of three of these degrees of freedom.
