- In mathematics, a
tangent vector is a
vector that is
tangent to a
curve or
surface at a
given point.
Tangent vectors are
described in the differential...
- setting, a
vector field gives a
tangent vector at each
point of the
manifold (that is, a
section of the
tangent bundle to the manifold).
Vector fields are...
-
defined as follows: T is the unit
vector tangent to the curve,
pointing in the
direction of motion. N is the
normal unit
vector, the
derivative of T with respect...
- In geometry, the
tangent line (or
simply tangent) to a
plane curve at a
given point is, intuitively, the
straight line that "just touches" the
curve at...
- the
tangent bundle of a
differentiable manifold M {\displaystyle M} is a
manifold T M {\displaystyle TM}
which ****embles all the
tangent vectors in M...
- the
tangent space at x {\displaystyle x} are
called the
tangent vectors at x {\displaystyle x} . This is a
generalization of the
notion of a
vector, based...
-
ordinary n-tuples can be used as well.
Definitions of
tangent vectors as
ordinary vectors A
tangent vector at a
point p may be defined, here
specialized to...
- the
covariant derivative is a way of
specifying a
derivative along tangent vectors of a manifold. Alternatively, the
covariant derivative is a way of...
- is a
tangent vector – a
vector at each point;
while the
value of the
derivative at a
point is a
cotangent vector – a
linear functional on
vectors. They...
- }}(t)\right|_{t=t_{0}}} is the
tangent vector at the
point P = γ(t0).
Generally speaking, the
tangent vector may be zero. The
tangent vector's magnitude ‖ γ ′ ( t...
