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The metacentric height is an approximation for the vessel stability at a small angle (0-15 degrees) of heel. Beyond that range, the stability of the vessel is dominated by what is known as a righting moment. Depending on the geometry of the hull, naval architects must iteratively calculate the center of buoyancy at increasing angles of heel.
In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation. [1]
Simpson's rules are used to calculate the volume of lifeboats, [6] and by surveyors to calculate the volume of sludge in a ship's oil tanks. For instance, in the latter, Simpson's 3rd rule is used to find the volume between two co-ordinates. To calculate the entire area / volume, Simpson's first rule is used. [7]
For a dynamical system with evolution equation ˙ = in an n–dimensional phase space, the spectrum of Lyapunov exponents {,, …,}, in general, depends on the starting point . However, we will usually be interested in the attractor (or attractors) of a dynamical system, and there will normally be one set of exponents associated with each ...
That is, perpendicular to the longitudinal stability axis. At low angles of attack, the lift is generated primarily by the wings, fins and the nose region of the body. The total lift acts at a distance ahead of the centre of gravity (it has a negative value in the figure), this, in missile parlance, is the centre of pressure . If the lift acts ...
The Lyapunov equation, named after the Russian mathematician Aleksandr Lyapunov, is a matrix equation used in the stability analysis of linear dynamical systems. [ 1 ] [ 2 ] In particular, the discrete-time Lyapunov equation (also known as Stein equation ) for X {\displaystyle X} is
Lyapunov stability of an equilibrium means that solutions starting "close enough" to the equilibrium (within a distance from it) remain "close enough" forever (within a distance from it). Note that this must be true for any ϵ {\displaystyle \epsilon } that one may want to choose.
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...