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Re[17]: Smeshenie perigeliya Merkuriya i drugih planet
17.01.2008 11:16 | V. V. Chazov

Dorogie druz'ya.
Shag za shagom reshim zadachu:
Dany
chislennye efemeridy Laboratorii reaktivnogo dvizheniya SShA.
Vychislit'
vektor polozheniya i vektor skorosti planety Merkurii otnositel'no Solnca 2 marta 2008 goda v 21 chas moskovskogo dekretnogo zimnego vremeni.
Reshenie
Polinomy Chebysheva T_n(x).
Opredeleny dlya znachenii x v intervale -1<=x<=+1.
T_0(x)=1, nachal'noe znachenie,
T_1(x)=x, nachal'noe znachenie,
a eto uzhe rekurrentnaya formula dlya lyubogo celogo polozhitel'nogo znacheniya n:
T_{n+2}(x)=2*x*T_{n+1}(x)-T_{n}(x).
Proizvodnye ot polinomov Chebysheva po peremennoi x opredeleny v tom zhe intervale -1<=x<=+1.
T'_0(x)=0, nachal'noe znachenie,
T'_1(x)=1, nachal'noe znachenie,
a eto uzhe rekurrentnaya formula dlya lyubogo celogo polozhitel'nogo znacheniya n:
T'_{n+2}(x)=2*x*T'_{n+1}(x)+2*T_{n+1}(x)-T'_{n}(x).
Esli izvesten moment vremeni t_c lezhashii v intervale t_a<=t_c<=t_b, to perehod k peremennoi x i intervalu -1<=x<=+1 vypolnyaetsya po formule:
x(t_c)=[t_c-0.5*(t_b+t_a)]/[0.5*(t_b-t_a)].
V efemeridah dlya kazhdoi iz koordinat dany chislennye znacheniya koefficientov
a_0, a_1, a_2, ... , a_m,
znachenie polozheniya po koordinate opredeleno formuloi:
r_x(t_c)=a_0*T_0(x(t_c))+a_1*T_1(x(t_c)) +a_2*T_2(x(t_c))+...a_m*T_m(x(t_c)),
znachenie skorosti po koordinate opredeleno formuloi:
v_x(t_c)=[a_0*T'_0(x(t_c))+a_1*T'_1(x(t_c)) +a_2*T'_2(x(t_c))+...a_m*T'_m(x(t_c))]*[(2*t_c)/(t_b-t_a)].
Edinica izmereniya polozhenii - kilometry.
Edinica izmereniya skorostei - kilometry za sutki.
Do vstrechi, Vash Vadim.


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