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  2. Euler's critical load - Wikipedia

    en.wikipedia.org/wiki/Euler's_critical_load

    The following assumptions are made while deriving Euler's formula: [3] The material of the column is homogeneous and isotropic. The compressive load on the column is axial only. The column is free from initial stress. The weight of the column is neglected. The column is initially straight (no eccentricity of the axial load).

  3. Eccentricity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Eccentricity_(mathematics)

    In mathematics, the eccentricity of a conic section is a non-negative real number that uniquely characterizes its shape. One can think of the eccentricity as a measure of how much a conic section deviates from being circular. In particular: The eccentricity of a circle is 0. The eccentricity of an ellipse which is not a circle is between 0 and 1.

  4. Column - Wikipedia

    en.wikipedia.org/wiki/Column

    The design of most classical columns incorporates entasis (the inclusion of a slight outward curve in the sides) plus a reduction in diameter along the height of the column, so that the top is as little as 83% of the bottom diameter. This reduction mimics the parallax effects which the eye expects to see, and tends to make columns look taller ...

  5. Orbital eccentricity - Wikipedia

    en.wikipedia.org/wiki/Orbital_eccentricity

    The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current epoch ) eccentricity of 0.011 3 , [ 13 ] but from 1800 to 2050 has a mean eccentricity of 0.008 59 .

  6. Two-body problem in general relativity - Wikipedia

    en.wikipedia.org/wiki/Two-body_problem_in...

    This may be simplified using the elliptical orbit's semi-major axis A and eccentricity e related by the formula (+) = to give the precession angle (+) () Since the closed classical orbit is an ellipse in general, the quantity A (1 − e 2 ) is the semi- latus rectum l of the ellipse.

  7. Eccentric anomaly - Wikipedia

    en.wikipedia.org/wiki/Eccentric_anomaly

    The eccentricity e is defined as: = . From Pythagoras's theorem applied to the triangle with r (a distance FP) as hypotenuse: = ⁡ + (⁡) = (⁡) + (⁡ + ⁡) = ⁡ + ⁡ = (⁡) Thus, the radius (distance from the focus to point P) is related to the eccentric anomaly by the formula

  8. Specific orbital energy - Wikipedia

    en.wikipedia.org/wiki/Specific_orbital_energy

    In the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy and their kinetic energy (), divided by the reduced mass. [1]

  9. Kepler's equation - Wikipedia

    en.wikipedia.org/wiki/Kepler's_equation

    As for instance, if the body passes the periastron at coordinates = (), =, at time =, then to find out the position of the body at any time, you first calculate the mean anomaly from the time and the mean motion by the formula = (), then solve the Kepler equation above to get , then get the coordinates from: