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In statics and structural mechanics, a structure is statically indeterminate when the equilibrium equations – force and moment equilibrium conditions – are insufficient for determining the internal forces and reactions on that structure.
In the classical central-force problem of classical mechanics, some potential energy functions () produce motions or orbits that can be expressed in terms of well-known functions, such as the trigonometric functions and elliptic functions. This article describes these functions and the corresponding solutions for the orbits.
The first nine blocks in the solution to the single-wide block-stacking problem with the overhangs indicated. In statics, the block-stacking problem (sometimes known as The Leaning Tower of Lire (Johnson 1955), also the book-stacking problem, or a number of other similar terms) is a puzzle concerning the stacking of blocks at the edge of a table.
In a broad sense, the term graphic statics is used to describe the technique of solving particular practical problems of statics using graphical means. [1] Actively used in the architecture of the 19th century, the methods of graphic statics were largely abandoned in the second half of the 20th century, primarily due to widespread use of frame structures of steel and reinforced concrete that ...
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
Statics is used in the analysis of structures, for instance in architectural and structural engineering. Strength of materials is a related field of mechanics that relies heavily on the application of static equilibrium. A key concept is the center of gravity of a body at rest: it represents an imaginary point at which all the mass of a body ...
Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L.
This is considered one of the simplest unsteady problems that has an exact solution for the Navier–Stokes equations. [ 1 ] [ 2 ] In turbulent flow, this is still named a Stokes boundary layer, but now one has to rely on experiments , numerical simulations or approximate methods in order to obtain useful information on the flow.
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