Cycloide curves
- x = (R + mR)cos(mt)
− hcos(t + mt)
- y = (R + mR)sin(mt)
− hsin(t + mt)
|
R=1; r=0.2; h=0.3; |
R=1; r=1; h=1.5 |
R=1; r=1/6; h=1+1/6 |
roots=0; width=200
fmin=-2-2i; fmax=2+2i
xmax=10*pi
R = 1; r=0.2; m=r/R
h=0.3
x=(R+m*R)*cos(m*t)-h*cos(t+m*t)
y=(R+m*R)*sin(m*t)-h*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t/5); color1=00aa00 |
roots=0; width=200
fmin=-4-4i; fmax=4+4i
xmax=2*pi
R = 1; r=1; m=r/R
h=1.5
x=(R+m*R)*cos(m*t)-h*cos(t+m*t)
y=(R+m*R)*sin(m*t)-h*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t);
color1=00aa00 |
roots=0; width=200
points=200
fmin=-3-3i; fmax=3+3i
xmax=12*pi
R = 1; r=1/6; m=r/R
h=1+1/6
x=(R+m*R)*cos(m*t)-h*cos(t+m*t)
y=(R+m*R)*sin(m*t)-h*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t/6);color1=00aa00 |
|
|
|
|
|
|
|
| R=1; r=0.2; h=0.1; |
R=1; r=0.1; h=0.1 |
|
roots=0; width=200
fmin=-2-2i;
fmax=2+2i
xmax=10*pi
R = 1; r=0.2; m=r/R
h=0.1
x=(R+m*R)*cos(m*t)-h*cos(t+m*t)
y=(R+m*R)*sin(m*t)-h*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t/5); color1=00aa00 |
roots=0; width=200
fmin=-2-2i; fmax=2+2i
xmax=10*pi
R = 1; r=0.2; m=r/R
h=0.2
x=(R+m*R)*cos(m*t)-h*cos(t+m*t)
y=(R+m*R)*sin(m*t)-h*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t/5); color1=00aa00 |
|
|
|
|
|
In Cartesian coordinates: (x2 + y2 - ay)2 = l2(x2+y2)
In polar coordinates:
r = l - a·sin(φ)
| a > l |
a = l |
a < l |
xmax=4*pi
fmin=-2-3i
fmax=2+i
l=1; a=2
r=l-a*sin(fi)
f(fi)=cplxe(r,fi) |
xmax=4*pi
fmin=-2-3i
fmax=2+i
l=1; a=1
r=l-a*sin(fi)
f(fi)=cplxe(r,fi) |
xmax=4*pi
fmin=-2-3i
fmax=2+i
l=1; a=0.5
r=l-a*sin(fi)
f(fi)=cplxe(r,fi) |
|
|
|
|
|
|
|
| l = 1/25 ... 2 |
|
|
nmax=50; animated(0,0)
xmax=4*pi
l=1; a=(n+1)/25
r=l-a*sin(fi)
f(fi)=cplxe(r,fi) |
|
|
|
|
|
|
x = (R + mR)cos(mt) - mcos(t + mt)
y = (R + mR)sin(mt) - msin(t + mt)
m=r/R;
| m = 1/10 |
m = 1/3 |
m = 2/3 |
roots=0; width=200
fmin=-1.5-1.5i; fmax=1.5+1.5i
xmax=20*pi
R = 1; m=1/10
x=(R+m*R)*cos(m*t)-m*cos(t+m*t)
y=(R+m*R)*sin(m*t)-m*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t/10); color1=00aa00 |
roots=0; width=200
fmin=-2-2i; fmax=2+2i
xmax=6*pi
R=1; m=1/3
x=(R+m*R)*cos(m*t)-m*cos(t+m*t)
y=(R+m*R)*sin(m*t)-m*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t/3); color1=00aa00 |
roots=0; width=200
fmin=-2.5-2.5i; fmax=2.5+2.5i
xmax=6*pi
R=1; m=2/3
x=(R+m*R)*cos(m*t)-m*cos(t+m*t)
y=(R+m*R)*sin(m*t)-m*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t/3); color1=00aa00 |
|
|
|
|
|
|
|
| m=1 |
|
|
roots=0; width=200
fmin=-3-3i; fmax=3+3i
R=1; m=1
x=(R+m*R)*cos(m*t)-m*cos(t+m*t)
y=(R+m*R)*sin(m*t)-m*sin(t+m*t)
XY(t)=x+i*y
XY1=exp(i*t); color1=00aa00 |
|
|
|
|
|
|
x=(R-mR)·cos(mt) + m·cos(t-mt)
y=(R-mR)·sin(mt) - m·sin(t-mt)
m=r/R;
| m = 1/4 |
m = 1/2.1 |
|
roots=0; width=200
xmax=8*pi
R=1; m=1/4
x=(R-m*R)*cos(m*t)+m*cos(t-m*t)
y=(R-m*R)*sin(m*t)-m*sin(t-m*t)
XY(t)=x+i*y
XY1=exp(i*t/4);
color1=00aa00 |
roots=0; width=200
xmax=42*pi
fmin=-1-i; fmax=1+i
R=1; m=1/2.1
x=(R-m*R)*cos(m*t)+m*cos(t-m*t)
y=(R-m*R)*sin(m*t)-m*sin(t-m*t)
XY(t)=x+i*y
XY1=exp(i*t/21);
color1=00aa00 |
|
|
|
|
|
x = r·t - h·sin(t)
y = r - h·cos(t)
| |
|
|
nmax=5; animated(100,0)
xmax=6*pi
width=400
r = 1; h=(n+1)/3
x=r*t-h*sin(t)
y=r-h*cos(t)
XY(t)=x+i*y |
a=0.4 %% a
=
0...1
fbox=1; width=400; ratio=1;
points=10; roots=0; spline=1
xmin=0; xmax=2*pi
p0=i+2*pi*a
p1=i+2*pi*a+exp(-i*2*pi*a+i*3*pi/2)
r = 1
x=r*(t-sin(t))
y=r*(1-cos(t))
XY(t)=x+i*y
XY1=(p0*(xmax-x)+p1*(x-xmin))/(xmax-xmin); color1=00aa00
XY2=i+2*pi*a+exp(-i*x); color2=00aa00 |
|
|
|
|
|
|
|
 |
|
Physical and
mathematical package "GRAPH"
