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The most important natural laws for structural engineering are Newton's Laws of Motion. Newton's first law states that every body perseveres in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.
So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion.
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
Newton has been called "the most influential figure in the history of Western science", [190] and has been regarded as "the central figure in the history of science", who "more than anyone else is the source of our great confidence in the power of science."
Education in mechanical engineering has historically been based on a strong foundation in mathematics and science. [ 44 ] In the 20th century, many governments began regulating both the title of engineer and the practice of engineering , requiring a degree from an accredited university and to past a qualifying test.
Newton's law of viscosity is the simplest relationship between the flux of momentum and the velocity gradient. It may be useful to note that this is an unconventional use of the symbol τ zx; the indices are reversed as compared with standard usage in solid mechanics, and the sign is reversed. [11]
"The theoretical development of the laws of motion of bodies is a problem of such interest and importance that it has engaged the attention of all the eminent mathematicians since the invention of the dynamics as a mathematical science by Galileo, and especially since the wonderful extension which was given to that science by Newton."
The configuration space and the phase space of the dynamical system both are Euclidean spaces, i. e. they are equipped with a Euclidean structure.The Euclidean structure of them is defined so that the kinetic energy of the single multidimensional particle with the unit mass = is equal to the sum of kinetic energies of the three-dimensional particles with the masses , …,:
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