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A soil reaction on the first (second) leg along the
OY
axis is as follows:
F
N
1(2)
=
F
1(2)
cos
μ
1(2)
.
(9)
The friction force magnitude on the second leg is determined
F
T
2
=
F
2
sin
μ
2
.
For determining the friction force on the first (second) leg, we shall
calculate its velocity along the
OX
axis:
V
x
1(2)
=
V
x
+
δV
x
1(2)
,
(10)
here
V
x
— is a velocity of the spacecraft center of mass along the
OX
axis;
δV
x
1(2)
=
−
V
y
(
α
1(2)
−
ϑ
)
— is a velocity of the leg during the shock
absorber length change;
δV
x
2
=
−
δV
2
cos
γ
2
and
δV
z
2
=
−
δV
2
sin
γ
2
— is
a displacement projection and a velocity of the second leg along the axes
OX
and
OZ
.
The friction force on the first and second legs can be calculated as
follows:
F
T
1
=
F
T
1
X
=
−
F
1
sin(
μ
1
)
V
x
1
abs
(
V
x
1
)
.
(11)
The third leg is symmetrical relative to the second leg; therefore, during
the longitudinal motion of the spacecraft landing on the surface of a celestial
body, the soil reaction forces on the second and the third legs are identical.
F
N
2
=
F
N
3
, F
TX
2
=
F
TX
3
.
(12)
Let us consider an example of using the proposed method for calculating
the parameters of the spacecraft longitudinal motion during landing on the
surface of the Moon [9, 10].
The design parameters of the spacecraft and the legs are:
m
= 900
kg,
I
z
= 800
kg
∙
m
2
,
h
0
= 0
.
38
m,
h
1
= 0
.
20
m,
H
= 1
.
06
m,
l
0
= 0
.
8
m,
l
E
= 1
.
0
m,
δ
0
= 0
.
001
m ,
F
0
= 3000
N.
We shall estimate the impact of different forces acting in the shock
absorbers during a vertical landing of the spacecraft under the following
conditions (
y
0
= 1
.
4
m,
V
y
0
= 0
.
1
,
V
x
0
= 0
,
μ
1
=
μ
2
= 0
.
2
,
ϑ
0
= 0
◦
,
θ
0
= 0
◦
). Fig. 5 shows graphs of variance of the soil normal reactions
on the legs of the spacecraft at
F
0
= 4000
N (variant 1),
F
0
= 3000
N
(variant 2),
F
0
= 2000
N (variant 3).
The graphs of variance analysis showed that in the first case, the soil
reaction force on the legs is very high and the strut inclination angle after
the spacecraft landing is rather large (
α
f
= 47
.
8
◦
). In the third case, the
ISSN 0236-3941. HERALD of the BMSTU. Series “Mechanical Engineering”. 2014. No. 1 31