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Clock angle problems relate two different measurements: angles and time. The angle is typically measured in degrees from the mark of number 12 clockwise. The time is usually based on a 12-hour clock . A method to solve such problems is to consider the rate of change of the angle in degrees per minute. The hour hand of a normal 12-hour analogue ...
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates ( x, y) with respect to the ...
Here, C is the difference between the angle moved at mean speed, and at the angle at the corrected speed projected onto the equatorial plane, and divided by 180° to get the difference in "half-turns". The value 23.44° is the tilt of the Earth's axis ("obliquity"). The subtraction gives the conventional sign to the equation of time.
Plot of one cycle of a sinusoidal function. The phase for each argument value, relative to the start of the cycle, is shown at the bottom, in degrees from 0° to 360° and in radians from 0 to 2π. In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function of some real variable (such as time) is an angle -like ...
Specifically, the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes and the third is an intrinsic rotation (a spin) around an axis fixed in the body that moves. Euler angles are typically denoted as α, β, γ, or φ, θ, ψ. This presentation is convenient only for rotations about a ...
Made in Germany, 1591. An equation clock is a mechanical clock which includes a mechanism that simulates the equation of time, so that the user can read or calculate solar time, as would be shown by a sundial. The first accurate clocks, controlled by pendulums, were patented by Christiaan Huyghens in 1657. For the next few decades, people were ...
In physics, Hooke's law is an empirical law which states that the force ( F) needed to extend or compress a spring by some distance ( x) scales linearly with respect to that distance—that is, Fs = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness ), and x is small compared to the total possible deformation of ...