Exploring the adaptation of Newton's laws to fluid dynamics, this overview delves into the Euler and Navier–Stokes equations, addressing viscosity and the challenges of singularities. It also touches on alternative classical mechanics formulations like Lagrangian and Hamiltonian mechanics, the Hamilton–Jacobi equation's role as a bridge to quantum mechanics, and the extension of Newtonian principles to thermodynamics and statistical physics through the kinetic theory of gases.
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1
The behavior of ______ bodies is described by Newton's laws of motion, which can be adapted for fluid study.
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2
The ______ derivative in the Euler equation accounts for the acceleration of fluid elements due to both temporal and spatial changes.
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3
Limitation of Euler equation in fluid dynamics
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4
Significance of Navier–Stokes in fluid dynamics
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5
Practical impact of viscous forces in fluid flow
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6
Newtonian mechanics faces challenges with ______, where its predictions can result in non-physical phenomena like infinite velocities.
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7
A ______ occurs when point masses are theoretically expelled to infinity in a limited amount of time, defying the principles of ______ and ______.
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8
Principle of least action in Lagrangian mechanics
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9
Role of Hamiltonian function
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10
Noether's theorem connection to mechanics
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11
In the - equation, the system's motion is depicted through an action function associated with the ______.
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12
Solutions to the - equation explain the system's dynamics with particle trajectories perpendicular to ______ action surfaces.
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13
The interpretation of mechanics as wave-like in the - equation is a forerunner to ______ mechanics.
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14
The - equation offers a conceptual bridge between ______ and modern physics.
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15
Kinetic theory of gases - Newtonian mechanics application
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16
Langevin equation purpose
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17
Newton's laws - Microscopic to macroscopic link
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