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Distributed hodograph of a coupler point of a four-bar linkage. Animation done using MeKin2D subroutines. [3] It is a method of presenting the velocity field of a point in planar motion. The velocity vector, drawn at scale, is shown perpendicular rather than tangent to the point path, usually oriented away from the center of curvature of the ...
Since the velocity of the object is the derivative of the position graph, the area under the line in the velocity vs. time graph is the displacement of the object. (Velocity is on the y-axis and time on the x-axis. Multiplying the velocity by the time, the time cancels out, and only displacement remains.)
Intuitively, the velocity increases linearly, so the average velocity multiplied by time is the distance traveled while increasing the velocity from v 0 to v, as can be illustrated graphically by plotting velocity against time as a straight line graph. Algebraically, it follows from solving [1] for
A plot of position and momentum variables as a function of time is sometimes called a phase plot or a phase diagram. However the latter expression, " phase diagram ", is more usually reserved in the physical sciences for a diagram showing the various regions of stability of the thermodynamic phases of a chemical system, which consists of ...
A Poincaré plot, named after Henri Poincaré, is a graphical representation used to visualize the relationship between consecutive data points in time series to detect patterns and irregularities in the time series, revealing information about the stability of dynamical systems, providing insights into periodic orbits, chaotic motions, and bifurcations.
Consider a smooth real-valued function of two variables, say f (x, y) where x and y are real numbers.So f is a function from the plane to the line. The space of all such smooth functions is acted upon by the group of diffeomorphisms of the plane and the diffeomorphisms of the line, i.e. diffeomorphic changes of coordinate in both the source and the target.
An illustration of the Frenet frame for a point on a space curve. T is the unit tangent, P the unit normal, and B the unit binormal. A Frenet frame is a moving reference frame of n orthonormal vectors e i (t) which are used to describe a curve locally at each point γ(t). It is the main tool in the differential geometric treatment of curves ...
The only line that fills the requirement is a line colinear with link P 1-A. Somewhere on this line there is a point P, the instant center of rotation for the body BAC. What applies to point A also applies to point B, therefore this instant center of rotation P is located on a line perpendicular to vector V B, a line colinear with link P 2-B.