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A hodograph is a diagram that gives a vectorial visual representation of the movement of a body or a fluid. It is the locus of one end of a variable vector, with the other end fixed. [1] The position of any plotted data on such a diagram is proportional to the velocity of the moving particle. [2] It is also called a velocity diagram.
Shock polar in the pressure ratio-flow deflection angle plane for a Mach number of 1.8 and a specific heat ratio 1.4. The minimum angle, , which an oblique shock can have is the Mach angle = (/), where is the initial Mach number before the shock and the greatest angle corresponds to a normal shock.
The Nyquist plot for () = + + with s = jω.. In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer Felix Strecker [] at Siemens in 1930 [1] [2] [3] and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, [4] is a graphical technique ...
On the momentum hodograph in the relevant section above, B is readily seen to connect the origin of momenta with the center of the circular hodograph, and to possess magnitude A/L. At perihelion, it points in the direction of the momentum. The vector B is denoted as "binormal" since it is perpendicular to both A and L. Similar to the LRL vector ...
Campbell Diagram of a steam turbine. Analysis shows that there are well-damped critical speed at lower speed range. Analysis shows that there are well-damped critical speed at lower speed range. Another critical speed at mode 4 is observed at 7810 rpm (130 Hz) in dangerous vicinity of nominal shaft speed, but it has 30% damping - enough to ...
The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...
One of the major usages of motion diagrams is to present film through a series of frames taken by a camera. Viewing an object on a motion diagram allows one to determine if an object is at a constant rest, speeding up, or slowing down. As the frames are taken, it can be assumed that an object is at a constant rest if it occupies the same ...
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.