Беляк О.А., Дрезин С.В. Динамика материальной точки
Подождите немного. Документ загружается.
>
>
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m (
d
2
dt
2
x(t)) = 0
m (
d
2
dt
2
y(t)) = −m g
>
>
>
x(0) = 0
D(x)(0) = V
0
cos(α)
y(0) = 0
D(y)(0) = V
0
sin(α)
>
>
>
x(t) = V
0
cos(α) t
y(t) = −
g t
2
2
+ V
0
sin(α) t
>
>
>
x 1 := x = V
0
cos(α) t
y 1 := y = −
g t
2
2
+ V
0
sin(α) t
>
>
>
y = −
1
2
x (g x − 2 sin(α) V
0
2
cos(α))
V
0
2
cos(α)
2
y = −
1
2
g x
2
V
0
2
cos(α)
2
+
sin(α) x
cos(α)
>
>
>
y1 := −
1
2
g x
2
V
0
2
cos(α)
2
+
sin(α) x
cos(α)
V
0
:= 10
α :=
π
4
g := 9.8
>
−.09800000000 x
2
+ x
>
>
>
>
>
0., 10.2040816 3
>
>
S 1 := 10 .2 0408163
>
>
>
x 1 := 5.102040815
H 1 := 2.551020408
mg
kmgv
>
>
>
>
m (
d
2
dt
2
x(t)) = −k m g D(x)
m (
d
2
dt
2
y(t)) = −m g − k m g D(y)
>
>
>
x(0) = 0
D(x)(0) = V
0
cos(α)
y(0) = 0
D(y)(0) = V
0
sin(α)
>
>
>
>
>
x(t) = −
V
0
cos(α) ( −1 + e
(−k g t)
)
k g
y(t) = −
e
(−k g t)
+ e
(−k g t)
V
0
sin(α) k + k g t − 1 −V
0
sin(α) k
k
2
g
>
>
>
>
x 2 := x = −
V
0
cos(α) (−1 + e
(−k g t)
)
k g
y 2 := y = −
e
(−k g t)
+ e
(−k g t)
V
0
sin(α) k + k g t − 1 −V
0
sin(α) k
k
2
g
>
>
>
y =
x k g + V
0
sin(α) k
2
x g + ln(
−x k g + V
0
cos(α)
V
0
cos(α)
) V
0
cos(α)
V
0
cos(α) k
2
g
y =
x
V
0
cos(α) k
+
sin(α) x
cos(α)
+
ln(
−x k g + V
0
cos(α)
V
0
cos(α)
)
k
2
g
>
>
>
>
V
0
:= 10
α :=
π
4
g := 9.8
k := .1
>
1.000000000
√
2 x + x + 10.20408163 ln(
(−.98 x + 5
√
2)
√
2
10
)
>
>
>
>
>
S 2 := 5.010064892, 0.
>
>
v y := 1 .000000000
√
2 + 1 −
9.999999997
−.98 x + 5
√
2
>
x H := 2.988706316
>
x := 2.98870 6316
>
H 2 := 1.758232486
>
>
y1 := −
1
2
g x
2
V
0
2
cos(α)
2
+
sin(α) x
cos(α)
>
>
y2 :=
x
k V
0
cos(α)
+ x tan(α) +
ln(
−k g x + V
0
cos(α)
V
0
cos(α)
)
k
2
g
>
V
0
:= 10
α :=
π
4
g := 9.8
k := .1
>
>
k = 0,1
×
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