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The three-body problem is a special case of the n-body problem, which describes how n objects move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n -body problem for details).
Suppose that X is a smooth complex algebraic variety.. Riemann–Hilbert correspondence (for regular singular connections): there is a functor Sol called the local solutions functor, that is an equivalence from the category of flat connections on algebraic vector bundles on X with regular singularities to the category of local systems of finite-dimensional complex vector spaces on X.
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
This procedure can be repeated to add F 3 to the resultant F 1 + F 2, and so forth. The parallelogram of forces is a method for solving (or visualizing) the results of applying two forces to an object. When more than two forces are involved, the geometry is no longer a parallelogram, but the same principles apply to a polygon of forces.
A graph of the vector-valued function r(z) = 2 cos z, 4 sin z, z indicating a range of solutions and the vector when evaluated near z = 19.5. A common example of a vector-valued function is one that depends on a single real parameter t, often representing time, producing a vector v(t) as the result.
The x direction may be chosen to point down the ramp in an inclined plane problem, for example. In that case the friction force only has an x component, and the normal force only has a y component. The force of gravity would then have components in both the x and y directions: mg sin( θ ) in the x and mg cos( θ ) in the y , where θ is the ...