Kinematics of a material point

For a description of a point s motion in space and time, a reference system should be chosen. The reference system is a collection of instmments the time-measuring device (e.g., a watch) and the bodies conditionally considered as being fixed in space with respect 

The reciprocal value p - 1/K is the curvature radius in point A. In fact, a circle s curvature is equal to its radius the curvature radius of a straight line is infinity. 

The simplest object in mechanics is called a material point (MP) this implies a body whose size in the framework of a given problem can be considered to be negligibly small. Another definition of an MP is that it is a point that possesses a mass. Different objects in different problems can be considered differently the molecules acting on a vessel s wall can be imagined as an MP, the earth moving around the sun may, in some instances, also be treated as an MP. However, the same objects in different problems cannot be considered 

An important task in kinematics is to assign an equation of motion, i.e., to construct the necessary mathematical equations that are sufficient to determine the MP s position in space at any instant of time. In the Cartesian coordinate system such an equation is the time dependence of the radius vector r(t) three scalar equations x(t), y t) and z t) correspond to one vector equation. 

The velocity at a given point is a physical value, numerically equal to the time derivative from the radius vector of the MP in the reference system under consideration. Remember that for brevity of writing, the time derivative function is denoted by a point above the letter, expressing a given function. 

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