On one resolvent method for integrating the low angle trajectories of a heavy point projectile motion under quadratic air resistance

New key parameters, namely $b_0 =\mathrm{tg}\,\theta_0, \theta_0$ — angle of throwing, $R_a$ — top curvature radius and $\beta_0$ — 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 $t(b), b =\mathrm{tg}\,\theta$ where $\theta$ is inclination angle. This method is based on Legendre transformation and its precision is automatically improved in wide range of the $\theta_0$ values and drag force parameters $\alpha$. The precision was monitored by Maple computing product.