By L. Huang
Statics and Dynamics of inflexible Bodies offers an interdisciplinary method of mechanical engineering via an in depth assessment of the statics and dynamics of inflexible our bodies, providing a concise advent to either. This quantity bridges the space of interdisciplinary released texts linking fields like mechatronics and robotics with multi-body dynamics for you to offer readers with a transparent route to knowing a variety of sub-fields of mechanical engineering. 3-dimensional kinematics, inflexible our bodies in planar areas and diverse vector and matrix operations are awarded with a view to offer a accomplished figuring out of mechanics via dynamics and inflexible bodies.
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Extra resources for A Concise Introduction to Mechanics of Rigid Bodies: Multidisciplinary Engineering
A pB/ means the position of B observed in universe frame fU g but described in frame fAg. • When the observation frame and the description frame are the same, the right subscript (the name of the observation frame) is not shown. For example: – ApB means the position of B observed and described in frame fAg. Remark. The above notations are defined using position vector as an example, but they can be used to represent any other types of vectors. , or a, it represents a linear velocity, an angular velocity, or a linear acceleration, respectively.
11, a rigid body rotates about the X axis of the universe frame. , ab) on the body projected on the plane perpendicular to the X axis (Y Z plane) and a principal axis (y) O on the same plane. The angular velocity ! D dÂ O i D ÂP iO: dt However, it is not so straightforward to describe the angular velocity if the rotation axis also changes with time. 26), angular velocity is related to the rate of change of the rotation matrix with respect to time. This provides a mechanism to find it. t C t/ D Rr .
It is related to the position of C observed and described in fAg through the following transformation: pC/A D RA ApC ; where RA is the rotation matrix of fAg with respect to fU g. B/A , and ˛B/A . ), which in many applications can be derived from analyzing simple linear or circular motions. 46 2 Kinematics Special Cases • Circular motion Referring to Fig. 2, a cylindrical coordinate frame is set up to describe circular motions. 67) are the axes of the cylindrical frame attached to point OA . 69) So the derivative of eOr is a vector aligning with eO , and vice versa.