Plane Kinematics of a Rigid Body.The ideal rigid body, is one in which the distance between any two points is invariable.
~ Three-dimensional Kinematics of a Rigid Body.The position of a rigid body is determined when we know the positions of three points A, B, C of it which are not colljnear, for the position of any other point P is then determined by the three distances PA, PB, PC. The nine co-ordinates (Cartesian or other) of A, B, C are subject to the three relations which express the invariability of the distances BC, CA, AB, and are therefote equivalent to six independent quantities.
The separation of kinematics from dynamics is due mainly to 0.
Franz Reuleauxs Kinematics of Machinery, translated by Sir A.
Then, by an obvious law of kinematics, the angular motion round the earth would be most rapid at the point nearest the earth, that is at perigee, and slowest at the point most distant from the earth, that is at apogee.
Also, everything relating to change of systems of axes, as for instance in the kinematics of a rigid system, where we have constantly to consider one set of rotations with regard to axes fixed in space, and another set with regard to axes fixed in the system, is a matter of troublesome complexity by the usual methods.
Plane kinematics of a rigid body.
Three-dimensional kinematics of a rigid body.
The proof is similar to that of the corresponding theorem of plane kinematics (~ 3).
Balls highly original investigations in kinematics and dynamics were published in collected form under the title Theory of Screws (Cambridge, 1900).
The modification of motion and the modification of force take place together, and are connected by certain laws; but in the study of the theory of machines, as well as in that of pure mechanics, much advantage has been gained in point of clearness and simplicity by first considering alone the principles of the modification of motion, which are founded upon what is now known as Kinematics, and afterwards considering the principles of the combined modification 01 motion and force, which are founded both on geometry and on the laws of dynamics.
PURE MEcHANISM, or APPLIED KINEMATIcs; being the theory of machines considered simply as modifying motion.
Division of the SubjectProceeding in the order of simplicity, the subject of Pure Mechanism, or Applied Kinematics, may be thus divided: Division 1.Motion of a point.
KINEMATICS (from Gr.