T:=evalf(4*Pi): > r:=vector([x,y,0]): > v:=map(diff,r,t); a:=map(diff,r,t$2); with(plots): Warning, the name changecoords has been redefined > pv:=0.01,0.05,0.2: > with(plottools) acc:=arrow(r1,a1,pv,color=red): vel:=arrow(r1,v1,pv,color=blue): txa:=TEXT([r[1]+a[1]*k,r[2]+a[2]],"a"): txv:=TEXT([r[1]+v[1]*k,r[2]+v[2]],"v") an:=norm(crossprod(v,a),2)/V: > t:=evalf(Pi)/2; := t 1.570796327 > ` x`=x;` an`=an; an .5883484054 > ` a`=a_;K:=24: > for i from 0 to K do t:=i/K*T: phi:=pi/4+t*omegaOA: x[1]:= OA*cos(phi): y[1]:= OA*sin(phi):x[2]:=x[1]: y[2]:=4*aP[i]:=display(box(5,2*a,4*a),box(4,3*a,2*a), Cir(1,r),Cir(7,r),Cir(5,r),Cir(4,r),Cir(3,R), Line(0,1,0),Line(7,8,0), Line(1,2,7),Line(7,6,7),Lin(5,4)PP:=display(seq(P[i],i=0..K),insequence=true, thickness=2, scaling=constrained, axes=none) restart:with(plots):with(plottools): N:=20 |
O‘zbekiston respublikasi oliy va o‘rta maxsus ta’lim vazirligi m. M. Mirsaidov, T. M. Sobirjonov nazariy mexanika
Pdf ko'rish
|
| bet | 170/177 | | Sana | 20.05.2024 | | Hajmi | 6,14 Mb. | | #245516 |
Bog'liq Nazariy Mexanika darslikBu sahifa navigatsiya:
- T:=evalf(4*Pi): > r:=vector([x,y,0]): > v:=map(diff,r,t); a:=map(diff,r,t$2);
- with(plots): Warning, the name changecoords has been redefined > pv:=0.01,0.05,0.2: > with(plottools)
- acc:=arrow(r1,a1,pv,color=red): vel:=arrow(r1,v1,pv,color=blue): txa:=TEXT([r[1]+a[1]*k,r[2]+a[2]],"a"): txv:=TEXT([r[1]+v[1]*k,r[2]+v[2]],"v")
- an:=norm(crossprod(v,a),2)/V: > t:=evalf(Pi)/2; := t 1.570796327 > ` x`=x;
- ` an`=an; an .5883484054 > ` a`=a_;
- K:=24: > for i from 0 to K do t:=i/K*T: phi:=pi/4+t*omegaOA: x[1]:= OA*cos(phi): y[1]:= OA*sin(phi):x[2]:=x[1]: y[2]:=4*a
- P[i]:=display(box(5,2*a,4*a),box(4,3*a,2*a), Cir(1,r),Cir(7,r),Cir(5,r),Cir(4,r),Cir(3,R), Line(0,1,0),Line(7,8,0), Line(1,2,7),Line(7,6,7),Lin(5,4)
- PP:=display(seq(P[i],i=0..K),insequence=true, thickness=2, scaling=constrained, axes=none)
- restart:with(plots):with(plottools): N:=20
restart:
>
N:=200:k:=.2:
>
x:=4-3*sin(t/2);
:=
x
4
3
sin
1
2
t
>
y:=5+2*cos(t/2);
:=
y
5
2
cos
1
2
t
>
T:=evalf(4*Pi):
>
r:=vector([x,y,0]):
>
v:=map(diff,r,t); a:=map(diff,r,t$2);
:=
v
,
,
3
2
cos
1
2
t
sin
1
2
t
0
:=
a
,
,
3
4
sin
1
2
t
1
2
cos
1
2
t
0
>
with(plots):
Warning, the name changecoords has been redefined
>
pv:=0.01,0.05,0.2:
>
with(plottools):
Warning, the name arrow has been redefined
>
for i to N do
t:=i/N*T+4:
r1:=vector([r[1],r[2]]):
v1:=vector([v[1],v[2]]):
a1:=vector([a[1],a[2]]):
acc:=arrow(r1,a1,pv,color=red):
vel:=arrow(r1,v1,pv,color=blue):
txa:=TEXT([r[1]+a[1]*k,r[2]+a[2]],"a"):
txv:=TEXT([r[1]+v[1]*k,r[2]+v[2]],"v"):
p[i]:=display(vel,acc,txa,txv): end do:
>
t:='t':
308
>
g1:=display(seq(p[i],i=1..N),insequence=true):
>
g2:=plot([x,y,t=0..T]):
>
display(g1,g2,scaling=constrained,title="Nuktaning tezligi va tezlanishi");
3.20-rasm
>
with(linalg):V:=norm(v,2):
Warning, the protected names norm and trace have been redefined and unprotected
>
at:=dotprod(v,a)/V:
>
a_:=norm(a,2):
>
an:=norm(crossprod(v,a),2)/V:
>
t:=evalf(Pi)/2;
:=
t
1.570796327
>
` x`=x;
x
1.878679656
>
` y`=y;
y
6.414213562
>
` v`=V;
v
1.274754878
>
` at`=at;
at
-.2451451688
>
` an`=an;
an
.5883484054
>
` a`=a_;
309
a
.6373774392
>
` ro`:=V^2/an;
:=
ro
2.761968902
3.3.1.Tekis parallel harakat
Koʻp zvenoli mexanizmlar texnikaning turli sohalari ( toʻqimachilik
mashinilari, mashinasozlik va boshqalar) da keng qoʻllaniladi. Nazariy mexanika
fanini oʻrganishda tekis parallel harakat qilayotgan koʻp zvenoli mexanizmlarning
harakatini animatsiyalar orqali namoish qilish shu tipdagi masalalarni tushinishda
katta ahamiyatga ega. Misol uchun
>
restart:
>
nam:=array(0..4,[O,A,B,D,C]):
>
read "ris.m";
>
OA:=2:AA:=7: a:=0.15: b:=3: BC:=10:R:=1.5:r:=0.1:
>
omegaOA:=2: T:=2*pi/omegaOA:
>
x[0]:=0:y[0]:=0:
>
with(plots):with(plottools):
Warning, the name changecoords has been redefined
Warning, the name arrow has been redefined
K:=24:
>
for i from 0 to K do t:=i/K*T: phi:=pi/4+t*omegaOA:
x[1]:= OA*cos(phi): y[1]:= OA*sin(phi):x[2]:=x[1]: y[2]:=4*a-
b:x[4]:=x[2]+BC: y[4]:=-b:x[3]:=BC/2:x[5]:=x[1]: y[5]:=-b: y[3]:=R-
b:x[6]:=x[1]: y[6]:=-4*a-b:
x[7]:=x[1]: y[7]:=y[1]-AA:
x[8]:=x[0]: y[8]:=y[0]-AA:
P[i]:=display(box(5,2*a,4*a),box(4,3*a,2*a),
Cir(1,r),Cir(7,r),Cir(5,r),Cir(4,r),Cir(3,R),
Line(0,1,0),Line(7,8,0),
Line(1,2,7),Line(7,6,7),Lin(5,4),
cir4(3,R,x[1]/R),
310
PLOT(seq(TEXT([x[j]+0.2,y[j]+0.7],nam[j]),j=0..4))):
od:
PP:=display(seq(P[i],i=0..K),insequence=true,
thickness=2,
scaling=constrained,
axes=none):
>
display(paverxnostь(5*R,-2.5*a-b,4*R,0.3),PP,Opora(0,0.1),
Opora(3,0.1),Opora(8,0.1));
3.21-rasm
Rasmda OA krivoshipdan harakat oluvchi va qismlari ilgarilanma, aylanma va
tekis parallel harakat qiluvchi mexanizm tasvirlangan.
6.1.4. Dinamika masalalarini matematik dasturlash.
Prujina koʻplab tebranma harakat qiladigan mashina va mexanizmlarda
qoʻllaniladi. Quyida bikrliklari turlicha boʻlgan ikkita prujinalarning
harakatlantirish dasturi tuzilgan.
>
restart:with(plots):with(plottools): N:=20:
Warning, the name changecoords has been redefined
Warning, the name arrow has been redefined
>
pru:=proc(x1,x2,y)local K,d,r,l: r:=6: K:=50: l:=(x2-x1)/3: d:=l/K:
|
| |
