integral curve वाक्य
उदाहरण वाक्य
मोबाइल
- We immediately obtain an integral curve which exhibits sinusoidal expansion and reconvergence cycles.
- In this example, the other integral curves are all simple closed curves.
- These integral curves are called the characteristic curves of the original partial differential equation.
- This hypotenuse is parallel to the tangent line of the integral curve at that corresponds to.
- In this formulation, the solutions of the Hamilton Jacobi equations are the integral curves of Hamiltonian vector fields.
- In other words, the graph of the solution must be a union of integral curves of this vector field.
- The geodesic lines are the projections of integral curves of the geodesic flow onto the manifold " M ".
- Integral curves are known by various other names, depending on the nature and interpretation of the differential equation or vector field.
- Associated to any Hamiltonian is a Hamiltonian vector field; the integral curves of the Hamiltonian vector field are solutions to Hamilton's equations.
- If the differential curve is the unit circle, the integral curve intersects the lines at points that are equally spaced at a distance of / 2.
- The integral curves of the timelike unit geodesic vector field \ vec { X } = \ vec { e } _ 0 give the world lines of our observers.
- Killing vector field whose integral curves are closed spacelike curves ( circles, in fact ), which moreover degenerate to zero length closed curves on the axis R = 0.
- In physics, integral curves for an electric field or magnetic field are known as field lines, and integral curves for the velocity field of a fluid are known as orbits.
- In physics, integral curves for an electric field or magnetic field are known as field lines, and integral curves for the velocity field of a fluid are known as orbits.
- It is solved by defining certain " kinematical quantities " which completely describe how the integral curves in a congruence may converge ( diverge ) or twist about one another.
- Assume furthermore that \ mu ^ {-1 } ( \ epsilon ) is fibered in circles, each of which is an integral curve of the induced Hamiltonian vector field.
- If the vector field X is nowhere zero then it defines a one-dimensional subbundle of the tangent bundle of M, and the integral curves form a regular foliation of M.
- One begins by noting that an arbitrary smooth vector field X on a manifold M defines a family of curves, its integral curves u : I \ to M ( for intervals I ).
- Thus, the problem of proving the existence and uniqueness of integral curves is the same as that of finding solutions to ordinary differential equations / initial value problems and showing that they are unique.
- The integral curves or fibers respectively are certain " pairwise linked " great circles, the orbits in the space of unit norm quaternions under left multiplication by a given unit quaternion of unit norm.
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