Результаты поиска по 'Legendre transformation':
Найдено статей: 2
  1. Chistyakov V.V.
    Numerical-analytical integrating the equations of a point mass projectile motion at the velocities close to sonic peak of air drag exponent
    Computer Research and Modeling, 2013, v. 5, no. 5, pp. 785-798

    It is shown that the relative air drag force for many different ballistic profiles obeys the law as follows R(V)=Mg·w(V/WT)n(V) with V being the velocity, WT — some threshold velocity close to that of sound, w equals to R(WT) and n(V) is the exponent in broken power Gȃvre formula. Using the Legendre transformation and in frames of perturbation approach received was the expression for addition δabb''(b) to resolvent function abb''(b), where a(b) is an intercept and b=tgθ, θ — inclination angle.

    Keywords: ballistic profile, power-law air resistance, exponent, sonic peak, Legendre transformation, resolvent function, perturbation approach, first term.
  2. Chistyakov V.V.
    On one resolvent method for integrating the low angle trajectories of a heavy point projectile motion under quadratic air resistance
    Computer Research and Modeling, 2011, v. 3, no. 3, pp. 265-277

    New key parameters, namely b0 = tgθ0, θ0 — angle of throwing, Ra — top curvature radius and β0 — dimensionless speed square on the top of low angular trajectory were suggested in classic problem of integrating nonlinear equations of point mass projectile motion with quadratic air drag. Very precise formulae were obtained in a new way for coordinates x(b), y(b) and fly time t(b), b = tgθ where θ is inclination angle. This method is based on Legendre transformation and its precision is automatically improved in wide range of the θ0 values and drag force parameters α. The precision was monitored by Maple computing product.

    Keywords: quadratic air drag, projectile, Legendre transformation, law angular trajectory, automatically adjusted formula precision, Maple.
    Views (last year): 1. Citations: 6 (RSCI).

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