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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.
In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors.
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 ...
Statics is the branch of classical mechanics that is concerned with the analysis of force and torque acting on a physical system that does not experience an acceleration, but rather is in equilibrium with its environment.
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.
Comparative statics was formalized by John R. Hicks (1939) and Paul A. Samuelson (1947) (Kehoe, 1987, p. 517) but was presented graphically from at least the 1870s. [2] For models of stable equilibrium rates of change, such as the neoclassical growth model, comparative dynamics is the counterpart of comparative statics (Eatwell, 1987).
The strength of materials is determined using various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus ...
[1] [2] The concept is essential, for instance, for understanding the net effect of multiple forces applied to a body. For example, if two forces of equal magnitude act upon a rigid body along the same line of action but in opposite directions, they cancel and have no net effect.