MATLAB


- 2


ax=diff(Vx,'t');

ay=diff(Vy,'t');

az=diff(Vz,'t');

a=sqrt(ax^2+ay^2);

at=(Vx*ax+Vy*ay+Vz*az)/V;

an=sqrt(a^2-at^2);

ro=V^2/an;

>> syms x y z t

>> x=-2*t^2+3;y=-5*t;z=3*t;

>> [Vx,Vy,Vz,V,ax,ay,az,a,at,an,ro]=cinema3d(x,y,z)

Vx =

-4*t

Vy =

-5

Vz =

3

V =

(16*t^2+34)^(1/2)

ax =

-4

ay =

0

az =

0

a =

4

at =

16*t/(16*t^2+34)^(1/2)

an =

4*(1-16*t^2/(16*t^2+34))^(1/2)

ro =

1/4*(16*t^2+34)/(1-16*t^2/(16*t^2+34))^(1/2)

ezplot3(x,y,z,[0,8])

t1

= 0,5 c

>> K=[Vx,Vy,Vz,V,ax,ay,az,a,at,an,ro];

>> t=0.5;

>> subs(K)

ans =

Columns 1 through 6

-2.0000 -5.0000 3.0000 6.1644 -4.0000 0

Columns 7 through 11

0 4.0000 1.2978 3.7836 10.0433

4.2

t1, c

x = x ( t ),

y = y ( t ),

1

- t 2 + 3

- 5 t

1/2

2

4 cos2(? t / 3) + 2

4 sin2(? t / 3) - 1

1

3

- cos(? t2 / 3) + 3

sin(? t2 / 3) - 1

1

4

4 t + 4

- 4 / (t + 1)

2

5

2 sin(? t / 3) 1

- 3 cos(? t / 3) + 4

1

6

3 t2 + 2

- 4 t

1/2

7

7 sin(? t2 / 6) + 3

2 - 7 cos(? t2 / 6)

1

8

- 3 / (t + 2)

3 t + 6

2

9

3 t2 t + 1

5 t2 5 t / 3 - 2

1

10

- 4 cos(? t / 3)

- 2 sin(? t / 3) 3

1

11

- 4 t2 + 1

- 3 t

1/2

12

5 sin2(? t / 6)

- 5 cos2(? t / 6) 3

1

13

5 cos(? t2 / 3)

- 5 sin(? t2 / 3)

1

14

- 2 t 2

- 2 / (t + 1)

2

15

4 cos(? t / 3)

- 3 sin(? t / 3)

1

16

3 t

4 t2 + 1

1/2

17

7 sin2(? t / 6) 5

- 7 cos2(? t / 6)

1

18

1 + 3 cos(? t2 / 3)

3 sin(? t2 / 3) + 3

1

19

- 5 t2 4

3 t

1

20

2 3 t 6 t2

3 3 t / 2 3 t2

0

21

6 sin(? t2 / 6) 2

6 cos(? t2 / 6) + 3

1

22

7 t2 3

5 t

1/4

23

3 3 t2 + t

4 5 t2 + 5 t / 3

1

24

- 4 cos(? t / 3) 1

- 4 sin(? t / 3)

1

25

- 6 t

- 2 t2 4

1

26

8 cos2(? t / 6) + 2

- 8 sin2(? t / 6) - 7

1

27

- 3 9 sin(? t2 / 6)

- 9 cos(? t2 / 6) + 5

1

28

- 4 t2 + 1

- 3 t

1

29

5 t2 + 5 t / 3 3

3 t2 + t + 3

1

30

2 cos(? t2 / 3) 2

- 2 sin(? t2 / 3) + 3

1