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A solution of the falling cat problem is a curve in the configuration space that is horizontal with respect to the connection (that is, it is admissible by the physics) with prescribed initial and final configurations. Finding an optimal solution is an example of optimal motion planning. [11] [12]
These terms are used in descriptions of engineering, physics, and other sciences, as well as ordinary day-to-day discourse. Though these terms themselves may be somewhat ambiguous, they are usually used in a context in which their meaning is clear. For example, when referring to a drive shaft it is clear what is meant by axial or radial directions.
This can be demonstrated by the following experiment: Hold a tennis racket at its handle, with its face being horizontal, and throw it in the air such that it performs a full rotation around its horizontal axis perpendicular to the handle (ê 2 in the diagram), and then catch the handle. In almost all cases, during that rotation the face will ...
The vector r(t) has some projection (or, equivalently, some component) r ⊥ (t) on a plane perpendicular to the axis of rotation. Then the angular position of that point is the angle θ from a reference axis (typically the positive x-axis) to the vector r ⊥ (t) in a known rotation sense (typically given by the right-hand rule).
An example of linear motion is an athlete running a 100-meter dash along a straight track. [2] Linear motion is the most basic of all motion. According to Newton's first law of motion, objects that do not experience any net force will continue to move in a straight line with a constant velocity until they are subjected to a net force.
Two methods of construction are obvious from Fig. 3-2: the x-axis is drawn perpendicular to the ct′-axis, the x′ and ct-axes are added at angle φ; and the x′-axis is drawn at angle θ with respect to the ct′-axis, the x-axis is added perpendicular to the ct′-axis and the ct-axis perpendicular to the x′-axis.
An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.) In the inertial frame of reference (upper part of the picture), the black ball moves in a straight line.
Example: A stone thrown into the air at an angle. Curvilinear motion describes the motion of a moving particles that conforms to a known or fixed curve. The study of such motion involves the use of two co-ordinate systems, the first being planar motion and the latter being cylindrical motion.