【物理应用】粒子在倒锥内部摩擦滑动的模拟和动画
【物理应用】粒子在倒锥内部摩擦滑动的模拟和动画
TT_Matlab
博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，完整matlab代码或者程序定制加qq1575304183。
1 简介
粒子在倒锥内部摩擦滑动的模拟和动画
2 完整代码
%% Particle sliding on the inside of an inverted cone
%
Simulation
and
animation of a particle sliding on the inside of an
% inverted cone with projections.
%
%%
clear ; close all ; clc
%
% Parameters
m =
1
; % Mass [kg]
c =
0
.
05
; % Drag coefficient [-]
g =
9.81
; % Gravity [m/s2]
parameters = [m c g];
%% Initial conditions
r0 = 2; %
Initial radial position [m]
th
0
=
0
; % Initial orientatio/n [rad]
dr
0
=
0
; % Initial radial speed [m/s]
dth
0
=
1
; % Initial angular speed [rad/s]
z
0
= [r
0
th
0
dr
0
dth
0
];
%% Simulation
tf = 30; %
Final time [s]
fR =
30
; % Frame rate [fps]
time = linspace(
0
,tf,tf*fR); % Time [s]
% Integration
[tout,xout] = ode45(@(t,z) particle(t,z,parameters),time,z
0
);
% Retrieving states
r = xout(
:
,
1
);
th = xout(
:
,
2
);
% Coordinates
z = r; % r=z. Cone angle =
45
deg.
x = r.*cos(th);
y = r.*sin(th);
%% Animation
color = cool(5); %
Colormap
gray_color = [
200
200
200
]/
255
;
L =
2.1
; % Distance form center
XYmin =-
2
;
XYmax =
4
;
Zmin = -
0
.
5
;
Zmax =
2.5
;
steptick =
1
;
figure
% set(gcf,
’Position’
,[
50
50
1280
720
]) %
YouTube:
720
p
% set(gcf,
’Position’
,[
50
50
854
480
]) %
YouTube:
480
p
set(gcf,
’Position’
,[
50
50
640
640
]) % Social
hold on ; grid on ; axis equal
set(gca,
’xlim’
,[XYmin XYmax],
’ylim’
,[XYmin XYmax],
’zlim’
,[Zmin Zmax])
set(gca,
’CameraPosition’
,[-
27.0446
-
27.4492
14.0294
])
set(gca,
’XTick’
,[XYmin XYmax],
’YTick’
,[XYmin XYmax],
’ZTick’
,[Zmin Zmax])
set(gca,
’XTickLabel’
,[],
’YTickLabel’
,[],
’ZTickLabel’
,[])
set(gca,
’FontName’
,
’Verdana’
,
’FontSize’
,
18
)
title([
"Particle sliding on the"
;
"inside of an inverted cone"
;
"Projections"
])
% Create
and
open video writer object
v = VideoWriter(
’particle_cone_projections.mp4’
,
’MPEG-4’
);
v.Quality =
100
;
v.FrameRate = fR;
open(v);
% Generating frames
for
i=
1
:length
(time)
cla
R = r
0
; % Radius
H = r
0
; % Height
N =
50
; % Number of points
[xCy, yCy, zCy] = cylinder([
0
R], N);
m = mesh(xCy, yCy, H*zCy);
set(m,
’edgealpha’
,
0
,
’facecolor’
,color(
1
,
:
),
’facealpha’
,
0
.
3
)
% Main particle
plot3(x(
1
:i
),y(
1
:i
),z(
1
:i
),
’Color’
,color(
5
,
:
),
’LineWidth’
,
2
)
plot3(x(i),y(i),z(i),
’ko’
,
’MarkerFaceColor’
,color(
5
,
:
),
’MarkerSize’
,
10
)
% Projections
plot3(x(
1
:i
),y(
1
:i
),Zmin*ones(i,
1
),
’Color’
,gray_color,
’LineWidth’
,
2
)
plot3(x(i),y(i),Zmin,
’o’
,
’Color’
,
’k’
,
’MarkerFaceColor’
,gray_color,
’MarkerSize’
,
10
)
plot3(XYmax*ones(i,
1
),y(
1
:i
),z(
1
:i
),
’Color’
,gray_color,
’LineWidth’
,
2
)
plot3(XYmax,y(i),r(i),
’o’
,
’Color’
,
’k’
,
’MarkerFaceColor’
,gray_color,
’MarkerSize’
,
10
)
plot3(x(
1
:i
),XYmax*ones(i,
1
),z(
1
:i
),
’Color’
,gray_color,
’LineWidth’
,
2
)
plot3(x(i),XYmax,z(i),
’o’
,
’Color’
,
’k’
,
’MarkerFaceColor’
,gray_color,
’MarkerSize’
,
10
)
frame = getframe(gcf);
writeVideo(v,frame);
end
close(v);
%% Auxiliary function
function dz = particle(~,z,dados)
%
Parametes
m = dados(
1
);
c = dados(
2
);
g = dados(
3
);
% States
r = z(
1
);
% th = z(
2
);
dr = z(
3
);
dth = z(
4
);
% State Equations
dz(
1
,
1
) = dr;
dz(
2
,
1
) = dth;
dz(
3
,
1
) = (-m*g + m*r*dth^
2
-
2
*c*dr)/(
2
*m);
dz(
4
,
1
) = (-
2
*m*dr*dth - c*r*dth)/(m*r);
end
3 仿真结果
4 参考文献
[1]周玲. "关于"滑动摩擦"教学动画模拟的尝试." 中学物理教学参考 7(1998).
博主简介：擅长智能优化算法、神经网络预测、信号处理、元胞自动机、图像处理、路径规划、无人机等多种领域的Matlab仿真，相关matlab代码问题可私信交流。
部分理论引用网络文献，若有侵权联系博主删除。