For studying the movement of some physical object (the car, the cyclist, a ball in a roulette) the movement of some of its points is enough to study. At a research of the movement it turns out that all points describe some curves.
Instruction
1. Know that curves it is possible to describe the movement of liquid, gas, light beams, lines of current. Curvature radius for a flat curve in a certain point is the radius of a tangent circle in this point. In certain cases the curve is set by the equations, and the radius of curvature is calculated on formulas. Respectively, to learn curvature radius, it is necessary to learn the radius of the circle concerning a certain point.
2. Define a point on the curve plane And, near it take one more point of V. Postroyte tangents to the available curve which pass through points And yes Century.
3. Carry out through points And yes To the lines perpendicular to the constructed tangents, prolong them up to crossing. Designate a point of intersection of perpendiculars as O. Tochka About is the center of a tangent circle in this point. OA – circle radius, i.e. curvature in this concrete point means And.
4. Let's notice that at the movement of a point on any curvilinear trajectory at any moment of the movement it moves on some circle which changes from a point to a point.
5. If for a point in space to define curvature in two mutually perpendicular directions, then these curvature will be called main. The direction main krivizn has to be obligatory for 900. For calculations often use the average curvature equal to the half-sum main krivizn, and the Gaussian curvature equal to their work. There is also a concept of curvature of a curve. It is size, the return to curvature radius.
6. Acceleration is an important factor of the movement of a point. The curvature of a trajectory directly influences acceleration. Acceleration arises when the point with a constant speed begins to move on a curve. Not only the absolute value of speed, but also its direction changes, there is a centripetal acceleration. I.e. the point begins to move to realities on a circle which concerns time at present.