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Newton's laws can be applied to fluids by considering a fluid as composed of infinitesimal pieces, each exerting forces upon neighboring pieces. The Euler momentum equation is an expression of Newton's second law adapted to fluid dynamics.
i.e. they take the form of Newton's second law applied to a single particle with the unit mass =.. Definition.The equations are called the equations of a Newtonian dynamical system in a flat multidimensional Euclidean space, which is called the configuration space of this system.
The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram metre per second (kg⋅m/s). The corresponding English engineering unit is the pound-second (lbf⋅s), and in the British Gravitational System, the unit is the slug-foot per second (slug⋅ft/s).
Euler's laws of motion are similar to Newton's laws, but they are applied specifically to the motion of rigid bodies. The Newton–Euler equations combine the forces and torques acting on a rigid body into a single equation. Newton's second law for rotation takes a similar form to the translational case, [13]
In special relativity, Newton's second law does not hold in the form F = ma, but it does if it is expressed as F = d p d t {\displaystyle \mathbf {F} ={\frac {d\mathbf {p} }{dt}}} where p = γ( v ) m 0 v is the momentum as defined above and m 0 is the invariant mass .
The above equation is often called d'Alembert's principle, ... By Newton's second law, the first time derivative of momentum is the force.
For a number of particles, the equation of motion for one particle i is: [7] ... For rigid bodies, Newton's 2nd law for rotation takes the same form as for translation:
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body.