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Axiomatic system of particle mechanics


m (r): m (~ 2 - O1) mu2 a mu1p2 a pI / ', / 7 is an I: △; (13) inferred by the force of two particles do not collide, the conservation of momentum after the collision. A proof based on particle collision forces and anti-particle force B were,, F, from (10),[link widoczny dla zalogowanych], we have: F: one of their impulse for the j: f. : A r-out: one of the 04) JllJ'l a muIsu by the momentum theorem for a mu u 'where mm respectively, the quality of the second particle. By (14) 'm a mul = a (m day L) is m ~ + m = m: m (15) before and after the second particle collisions conservation of momentum. For the explosive situation there on the three particle momentum conservation law, multi-particle case is also true. Definition 5 power: the force acting on the particle displacement and particle scalar product, for the force on the particles for power, with that, then. d: f A F. d-r) (16) 1 Zhu Peiyi, etc.: The axiomatic system of particle mechanics the kinetic energy of 43 Definition 6: Particle mass and particle velocity is called the square of half the product of the function of the particle (non-relativistic case), with that, then; 1: 2 (17) Theorem 3 for the work force on the particle kinetic energy is equal to the increase of the particle, the theorem is also known as kinetic energy theorem. Prove = dr == mr2d_. v_. dsarm · surface dv = m == △ Definition 7 Torque: position vector r and force F of the vector product, if used, said workers = r × F is defined in 8 angular momentum, also called moment of momentum, position vector r and momentum P, vector product, to G, then G = rP Theorem 4 point 0, the particle angular momentum on the time rate of change equal to the external torque on the fixed-point proved = m, × = × z =×=×( m (1 (19) (20): A: (21) If a L21J inference torque force on the particle is 0, then the conservation of angular momentum, this is the law of conservation of angular momentum. 4, the definition of conservation of mechanical energy conservative forces 9: If the integration of space power has nothing to do with the path, that is, if f '· d; = 』-F. d; (22) is called a conservative force. Easy to show that integration of space forces and the force has nothing to do with the path integral on the closed curve is zero is equivalent to a week. Theorem 5 If the conservative forces, can be written as a scalar function of the negative gradient. Prove that f; 'a = 』? (A + a + a from the mathematical analysis, such as fr2. d; integrable the Gansu Education College (Natural Science) Volume No. l2 』· a; = a』; a (,,,)= a, r2, 0t ~ a + +8: vd =) and d, d can be any value, so there are = a = side = one love (23) that F = a VV (24) reasoning, such as F = a vV, then the force F as a conservative force. Proved slightly. Definition of 10 potential energy: If F = a vV, then V is called potential energy of the particle in r at. Theorem 6 If F in an area without singularity, F has continuous partial space derivative in a single connected region, the force of the curl is zero everywhere, the same force is conservative force is equivalent to prove omitted. 1l define mechanical energy: kinetic and potential energy of the particles and, as the mechanical energy of the particle, with E said. Theorem 7 If the role only by conservative forces, the particle's mechanical energy remains unchanged. Proved by (1 dr = l a a T1 · d; = a 『v. d:, 2 a l-dv = a V14-V is a T = a (V a) +: T1 + V (25) E2 = EI namely the law of conservation of mechanical energy. System is still based on the above theory on the basis of absolute space and time, its scope is still a low speed area. If the above theory is applied to particle mechanics of particles, rigid bodies, continuous media, you can get the mechanical system of particles, rigid body mechanics, continuum mechanics of a theorem, corollary, the formula and so on.