Definitions

1. The velocity vector is a displacement vector (a polar vector) divided by time (a scalar), so is also a polar vector.
2. This velocity vector is perpendicular to the position vector, and it is tangent to the circular path of the moving object.
3. The velocity vector, the acceleration vector, and the local center of curvature of path lie in the osculating plane.
4. The areal velocity vector is perpendicular to this surface, and, in general, varies in both magnitude and direction.
5. The areal velocity vector is always perpendicular to the conical surface and is proportional to the angular momentum of the particle.

Differentiable Vector

1. Let r(t) be a differentiable vector valued function and v(t) = r '(t) be the velocity vector.

Vector Dot Product

1. Note that we use vector dot product to square the velocity vector.

Angular Velocity Vector

1. Angular acceleration vector does not always point in the direction of the angular velocity vector.

Dimensions

1. Three-holes arranged in a line allow the pressure probes to measure the velocity vector in two dimensions.

Proportional

1. More formally, in this situation the velocity vector r ′(t) and the acceleration vector r ′′(t) are required not to be proportional.

Product

1. It is expressed as the product of the moment of inertia of the object and its angular velocity vector.

Geodesic

1. Since v corresponds to the velocity vector of the geodesic, the actual (Riemannian) distance traveled will be dependent on that.
2. Theorem 1 (Euler-Arnold equation) Let be a geodesic flow on using the right-invariant metric defined above, and let be the intrinsic velocity vector.

Polar Vector

1. Likewise, the momentum vector is the velocity vector (a polar vector) times mass (a scalar), so is a polar vector.

Tangent Bundle

1. An element of the tangent bundle is interpreted as a velocity vector.

Angle

1. The angle between the velocity vector and the radius vector (vertical) or the complement of this angle (horizontal).

Constant

1. In others, only a component of the areal velocity vector is constant.

Speed

1. If we consider the flow of a fluid in a region, the velocity vector field indicates the speed and direction of the flow of the fluid at that point.
2. The Maxwell-Boltzmann distribution for the speed follows immediately from the distribution of the velocity vector, above.

Tangential

1. However, it must be remembered that the velocity vector can be also decomposed into tangential and normal components.

Orbital Velocity

1. The angle between the sail surface normal and the velocity vector that is optimal for reducing the orbital velocity is 35°.

Orbital Plane

1. Orbital Plane The plane containing the centre of mass of the earth and the velocity vector (direction of motion) of a satellite.

Unit Tangent Vector

1. Then we define the unit tangent vector by as the unit vector in the direction of the velocity vector.

Time

1. The instantaneous velocity of a particle is defined as the first derivative of the position vector with respect to time,, termed the velocity vector,.
2. Therefore the spin angular velocity vector (ω s) about the spin axis will have to evolve in time so that the matrix product L = I. ω s remains constant.

Orbits

1. We already have two funamental vectors that are used to analyze orbits: the position vector r, and the velocity vector v.

Orbit

1. In planar problems, such as the orbit of a planet about the sun, the direction of the areal velocity vector is perpendicular to the orbital plane.

Change

1. The first integral contains the Convective derivative of the velocity vector, and the second integral contains the change and flow of mass in time.
2. To achieve desired conditions according to the invention, the total change in velocity vector.DELTA.V required for eccentricity control is first determined.
3. This maneuver requires a change in the orbital velocity vector (delta v) at the orbital nodes (i.e.

Curve

1. Parametric representation of a curve in sapce, velocity vector, covariant derivative.

Axis

1. The positive X axis, in aircraft, points along the velocity vector, in missiles and rockets it points towards the nose.
2. The angular velocity vector also describes the direction of the axis of rotation.
3. The angular velocity vector also points along the axis of rotation in the same way as the angular displacements it causes.

X-Axis

1. Consider a spacecraft local frame where the y-axis points towards the Earth and the x-axis lies in the orbit plane in the direction of the velocity vector.

Space

1. The areal velocity vector can be placed at the moving point B. As the particle moves along its path in space, it sweeps out a cone-shaped surface.

Intuitively

1. Explicitly, in any (and hence all) coordinate charts φ. Intuitively, the equivalence classes are curves through p with a prescribed velocity vector at p.

Magnitude

1. The change in angular velocity is perpendicular to the angular velocity vector, changing its direction but not its magnitude.
2. For the first 5s the magnitude of the velocity vector increases at a constant rate.

Vector

1. A vector is a unit with both a magnitude and a direction-- i.e., a car traveling 50 mph due east would have a velocity vector.

Direction

1. The magnitude of the radial velocity is the dot product of the velocity vector and the unit vector in the direction of the displacement.
2. The magnitude of the transverse velocity is that of the cross product of the unit vector in the direction of the displacement and the velocity vector.
3. Momentum is a vector quantity; i.e., it has both a magnitude and a direction, the direction being the same as that of the velocity vector.

Longitudinal Axis

1. Angle of attack: The angle between the velocity vector and the longitudinal axis of a missile or rocket.

Point

1. The vector field v(x) is a smooth function that at every point of the phase space M provides the velocity vector of the dynamical system at that point.
2. Note that at point the curve is parallel to the flow velocity vector, where the velocity vector is evaluated at the position of the particle at that time t.
3. In this case, a velocity vector is associated to each point in the fluid.

Tangent

1. For any object moving through space, the velocity vector is tangent to the trajectory.

Streamline

1. A streamline is a line that is tangent to the velocity vector of the flowing fluid.

Streamlines

1. Since streamlines are tangent to the velocity vector of the flow, the value of the stream function must be constant along a streamline.
2. In fluid dynamics, streamlines are a family of curves that are instantaneously tangent to the velocity vector of the flow.

Velocity Vector

1. To change the orbit of a space vehicle, we have to change its velocity vector in magnitude or direction.
2. A streamline is a curve whose tangent at any point is in the direction of the velocity vector at that point.
3. The tangential component a t is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector.

Categories

1. Algebra > Linear Algebra > Vectors > Position Vector
2. Algebra > Linear Algebra > Vectors > Unit Vector
3. Vector Field
4. Streamlines
5. Science > Mathematics > Geometry > Tangent
6. Books about "Velocity Vector" in Amazon.com
   

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