Briefly compare Langrange-Euler and Newton-Euler approach.
Answers
Answered by
1
MARK BRAINLIEST
The term "Lagrangian" has several different meanings in the mathematical sciences. But as you are contrasting it with an "Eulerian" approach, I think that your question refers to the system of coordinates used in fluid mechanics.There are two ways to characterize a flow mathematically. One way is to indicate the velocity, as a function of time, for each individual fluid element (i.e., for each little bit of mass in the fluid). You might imagine placing a very tiny drop of dye into a stream of water and following the dye around, indicating the direction and speed with which it is moving at any given time. This corresponds to describing the flow using Lagrangian coordinates.Another approach would be to define coordinates that are fixed in a laboratory frame (for instance, which are defined with respect to the walls of a solid tank), and then to indicate the velocity of the fluid element that is flowing past a given point in that coordinate system, at a given time. As the little drop of dye moves around, its motion will be described by the values of the velocity field evaluated at successively different points, each corresponding to the dye's instantaneous location with respect to the tank.For most practical applications, Eulerian coordinates are more useful than Lagrangian ones. But the fact that Newton's laws of motion refer to individual fluid elements, whose positions are changing in the Eulerian coordinates, is one of the things that makes the mathematics of fluid mechanics significantly more complicated than that of solids.
The term "Lagrangian" has several different meanings in the mathematical sciences. But as you are contrasting it with an "Eulerian" approach, I think that your question refers to the system of coordinates used in fluid mechanics.There are two ways to characterize a flow mathematically. One way is to indicate the velocity, as a function of time, for each individual fluid element (i.e., for each little bit of mass in the fluid). You might imagine placing a very tiny drop of dye into a stream of water and following the dye around, indicating the direction and speed with which it is moving at any given time. This corresponds to describing the flow using Lagrangian coordinates.Another approach would be to define coordinates that are fixed in a laboratory frame (for instance, which are defined with respect to the walls of a solid tank), and then to indicate the velocity of the fluid element that is flowing past a given point in that coordinate system, at a given time. As the little drop of dye moves around, its motion will be described by the values of the velocity field evaluated at successively different points, each corresponding to the dye's instantaneous location with respect to the tank.For most practical applications, Eulerian coordinates are more useful than Lagrangian ones. But the fact that Newton's laws of motion refer to individual fluid elements, whose positions are changing in the Eulerian coordinates, is one of the things that makes the mathematics of fluid mechanics significantly more complicated than that of solids.
Answered by
0
Answer:
Euler's identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as "the most beautiful equation." It is a special case of a foundational equation in complex arithmetic called Euler's Formula, which the late great physicist Richard Feynman called in his lectures "our .
Explanation:
Similar questions