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Aircraft flight dynamics. Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of gravity (cg), known as pitch, roll and yaw. These are collectively known as aircraft attitude, often ...
A top whose axis is situated along the binormal is observed to rotate with angular speed κ. If the axis is along the tangent, it is observed to rotate with angular speed τ. Concretely, suppose that the observer carries an (inertial) top (or gyroscope) with them along the curve. If the axis of the top points along the tangent to the curve ...
The point E is an arbitrary point on the parabola. The focus is F, the vertex is A (the origin), and the line FA is the axis of symmetry. The line EC is parallel to the axis of symmetry, intersects the x axis at D and intersects the directrix at C. The point B is the midpoint of the line segment FC.
The polar angle may be called inclination angle, zenith angle, normal angle, or the colatitude. The user may choose to ignore the inclination angle and use the elevation angle instead, which is measured upward between the reference plane and the radial line—i.e., from the reference plane upward (towards to the positive z-axis) to the radial line.
If = + is the distance from c 1 to c 2 we can normalize by =, =, = to simplify equation (1), resulting in the following system of equations: + =, + =; solve these to get two solutions (k = ±1) for the two external tangent lines: = = + = (+) Geometrically this corresponds to computing the angle formed by the tangent lines and the line of ...
Illustration of tangential and normal components of a vector to a surface. In mathematics, given a vector at a point on a curve, that vector can be decomposed uniquely as a sum of two vectors, one tangent to the curve, called the tangential component of the vector, and another one perpendicular to the curve, called the normal component of the vector.
The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
Additionally, axis–angle extraction presents additional difficulties. The angle can be restricted to be from 0° to 180°, but angles are formally ambiguous by multiples of 360°. When the angle is zero, the axis is undefined. When the angle is 180°, the matrix becomes symmetric, which has implications in extracting the axis.
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