1 Correction to: Celest Mech Dyn Astr (2017) 128:483–513 DOI 10.1007/s10569-017-9758-8
In the paper Nerovny et al. (2017), the commentaries about a convergence of series which represent the absolute value function and corresponding equations contain several mistakes (Sect. 2, from Eqs. (4) to (6)).
The series Eq. (3)
of Chebyshev polynomials of the first kind for \(|\hat{\mathbf {n}}\cdot \hat{\mathbf {s}}|=|x|\le 1\) is absolutely convergent. If we define \(x=\cos y\), than \(T_{2n}=\cos 2ny\), \(|T_{2n}|\le 1\), and we get the ordinary Fourier series which is majorizable by the following convergent series:
Additionally, for any x the original series is an alternating Leibniz series. Its partial sum differs from |x| less or equal than the absolute value of the first neglected term.
These are the steps to produce a power series of absolute value function from Eq. (3):
That’s why the Eqs. (4) and (5) from Nerovny et al. (2017) should be written as follows:
and in equations for \(N_{\max B}\), Eqs. (6) and (34), the \(\lfloor (N_{\max }-1)/2 \rfloor \) term should be replaced by \(N_{\max }\).
The results of calculations in Sects. 7 and 8 are not affected by this error because in the numerical calculations we used correct relations presented in this erratum.
Reference
Nerovny, N., Zimin, V., Fedorchuk, S., Golubev, E.: Representation of light pressure resultant force and moment as a tensor series. Celest. Mech. Dyn. Astron. 128, 483–513 (2017). doi:10.1007/s10569-017-9758-8
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The online version of the original article can be found under doi:10.1007/s10569-017-9758-8.
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Nerovny, N., Zimin, V., Fedorchuk, S. et al. Correction to: Representation of light pressure resultant force and moment as a tensor series. Celest Mech Dyn Astr 129, 555–556 (2017). https://doi.org/10.1007/s10569-017-9791-7
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DOI: https://doi.org/10.1007/s10569-017-9791-7