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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. [1] [2]
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.
McGraw-Hill purchased Schaum Publishing Company in 1967. [2] Titles are continually revised to reflect current educational standards in their fields, including updates with new information, additional examples, use of new technology (calculators and computers), and so forth. New titles are also introduced in emerging fields such as computer ...
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 ...
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities. Sometimes called statistical physics or statistical thermodynamics, its applications include many problems in the fields of physics, biology, [1] chemistry, neuroscience, [2] computer science, [3] [4] information theory [5] and ...
Example with infinitely many solutions: 3x + 3y = 3, 2x + 2y = 2, x + y = 1. Example with no solution: 3 x + 3 y + 3 z = 3, 2 x + 2 y + 2 z = 2, x + y + z = 1, x + y + z = 4. These results may be easier to understand by putting the augmented matrix of the coefficients of the system in row echelon form by using Gaussian elimination .
Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium [1] and "the pressure in a fluid or exerted by a fluid on an immersed body". [ 2 ] It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics , the study of fluids in motion.
The envelope theorem is an important tool for comparative statics of optimization models. [ 2 ] The term envelope derives from describing the graph of the value function as the "upper envelope" of the graphs of the parameterized family of functions { f ( x , ⋅ ) } x ∈ X {\displaystyle \left\{f\left(x,\cdot \right)\right\}_{x\in X}} that are ...