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Average acceleration. Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as time interval Δt → 0 of Δv/Δt.
Streamlines are defined by [4] =, where "" denotes the vector cross product and () is the parametric representation of just one streamline at one moment in time. If the components of the velocity are written = (,,), and those of the streamline as = (,,), we deduce [4] = =, which shows that the curves are parallel to the velocity vector.
In navigation, dead reckoning is the process of calculating the current position of a moving object by using a previously determined position, or fix, and incorporating estimates of speed, heading (or direction or course), and elapsed time. The corresponding term in biology, to describe the processes by which animals update their estimates of ...
Working in CGS units, we first need to find the form of the electric and magnetic fields. The fields can be written (for a fuller derivation see Liénard–Wiechert potential) (,) = (()) + ([() ˙] ()) and =, where is the charge's velocity divided by , ˙ is the charge's acceleration divided by c, is a unit vector in the direction, is the magnitude of , is the charge's location, and = /.
Stream function. Streamlines – lines with a constant value of the stream function – for the incompressible potential flow around a circular cylinder in a uniform onflow. In fluid dynamics, two types of stream function are defined: The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in 1781, [1] is defined ...
To state this formally, in general an equation of motion M is a function of the position r of the object, its velocity (the first time derivative of r, v = dr dt), and its acceleration (the second derivative of r, a = d2r dt2), and time t. Euclidean vectors in 3D are denoted throughout in bold.
Gravity turn. A gravity turn or zero-lift turn is a maneuver used in launching a spacecraft into, or descending from, an orbit around a celestial body such as a planet or a moon. It is a trajectory optimization that uses gravity to steer the vehicle onto its desired trajectory. It offers two main advantages over a trajectory controlled solely ...
Time-derivatives of position. In physics, the fourth, fifth and sixth derivatives of position are defined as derivatives of the position vector with respect to time – with the first, second, and third derivatives being velocity, acceleration, and jerk, respectively. The higher-order derivatives are less common than the first three; [ 1 ][ 2 ...