# PHYS 1111L Lecture Notes - Lecture 6: Analytical Dynamics, Algebraic Geometry, Mechanical Engineering

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KINEMATICS

Kinematics is a branch of classical mechanics that describes the motion of points, bodies

(objects), and systems of bodies (groups of objects) without considering the mass of each

or the forces that caused the motion. Kinematics, as a field of study, is often referred to as

the "geometry of motion" and is occasionally seen as a branch of mathematics.A kinematics

problem begins by describing the geometry of the system and declaring the initial conditions

of any known values of position, velocity and/or acceleration of points within the system.

Then, using arguments from geometry, the position, velocity and acceleration of any

unknown parts of the system can be determined. The study of how forces act on masses

falls within kinetics. For further details, see analytical dynamics.

Kinematics is used in astrophysics to describe the motion of celestial bodies and collections

of such bodies. In mechanical engineering, robotics, and biomechanics kinematics is used to

describe the motion of systems composed of joined parts (multi-link systems) such as an

engine, a robotic arm or the human skeleton.

Geometric transformations, also called rigid transformations, are used to describe the

movement of components in a mechanical system, simplifying the derivation of the equations

of motion. They are also central to dynamic analysis.

Kinematic analysis is the process of measuring the kinematic quantities used to describe

motion. In engineering, for instance, kinematic analysis may be used to find the range of

movement for a given mechanism, and working in reverse, using kinematic synthesis to

design a mechanism for a desired range of motion. In addition, kinematics applies algebraic

geometry to the study of the mechanical advantage of a mechanical system or mechanism.

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