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Weak form and strong form may refer to: Weaker and stronger versions of a hypothesis, theorem or physical law; Weak formulations and strong formulations of differential equations in mathematics; Differing pronunciations of words depending on emphasis; see Weak and strong forms in English; Weak and strong pronouns
In a weak formulation, equations or conditions are no longer required to hold absolutely (and this is not even well defined) and has instead weak solutions only with respect to certain "test vectors" or "test functions". In a strong formulation, the solution space is constructed such that these equations or conditions are already fulfilled.
Weakened weak form (or W2 form) [1] is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings. These numerical methods are applicable to solid mechanics as well as fluid dynamics problems.
Good form ensures that the movement only uses the main muscles, and avoids recruiting secondary muscles. As a muscle fatigues, the body attempts to compensate by recruiting other muscle groups and transferring force generation to non-fatigued units.
Weight-bearing exercise also helps to prevent osteoporosis and to improve bone strength in those with osteoporosis. [70] For many people in rehabilitation or with an acquired disability, such as following stroke or orthopaedic surgery, strength training for weak muscles is a key factor to optimise recovery. [71]
Ritz–Galerkin method (after Walther Ritz) typically assumes symmetric and positive definite bilinear form in the weak formulation, where the differential equation for a physical system can be formulated via minimization of a quadratic function representing the system energy and the approximate solution is a linear combination of the given set ...
Aerobics is a form of physical exercise that combines rhythmic aerobic exercise with stretching and strength training routines with the goal of improving all elements of fitness (flexibility, muscular strength, and cardio-vascular fitness).
Exercise – any bodily activity that enhances or log physical fitness and overall health and wellness. It is performed for various reasons including strengthening muscles and the cardiovascular system , honing athletic skills, weight loss or maintenance, as well as for the purpose of enjoyment.