About Pushbutton Stop

8/12/2019 About Pushbutton Stop

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Lab 1, EME 121, UC Davis, Spring 2011

Nasser M. Abbasi

Contents

1 Problem description 2

2 Mathematical model 4

3 Result of simulation 5

4 Discussion of results 8

5 Appendix 8

5.1 Source code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

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1 Problem description

We are asked to write a program to simulation the equation of motion of the following springpendulum shown in the textbook on page 42

Notice that the r generalized coordinate is measured from the corner where the springis attached to and not from the static equilibrium position. This diagram below helps to

illustrate this more.

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Now the equations of motion are found and then they are converted to state form descriptionand then ODE solver was used to integrate them.

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2 Mathematical model

This system is 2 degree of freedom system, since two generalized coordinates are required touniquely locate the massmat any point of time. Hence, two EQMs (equation of motions)are required.

ApplyingF =ma in the radial spring direction results in the following EQM

T+mg cos = m(r r ()2)

Rearranging, and noting thatT =k (r l0) we obtain

r =r ()2

+g cos k

m(r l0) (1)

ApplyingF = ma in the perpendicular direction to the spring results in the followingEQM

mg sin = m (r + 2r)

= g

rsin

2r

r (2)

To use the ODE solver, the above second order ODEs, Eqs., (1) and (2), need to beconverted to first order ODE. This is done by introducing state variables as follows

x1= r

x2= r

x3=

x4=

d

dt

x1

= x2

x2

= x1x2

4+g cos x3

km

(x1 l0)

x3

= x4

x4

= grsin x3

2x2x4x1

Therefore, the state space form is

x1

x2

x3

x4

=

x2

x1x2

4+g cos x3

km

(x1 l0)

x4

g

rsin x3

2x2x4x1

(3)

The above system is solved using ODE solver and the result are shown in the followingsection.

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3 Result of simulation

Using the following parameters to generate figure (3.2) and figure 3.3 for the very stiff spring

m f l0

r (0) r

(0) (0)

(0)

5kg 1000 Hz 1 m 1 m 0 450 0

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Using the following parameters to generate figure (3.4)

m f l0 r (0) r (0) (0) (0)

5kg 1 Hz 1 m 1 m 0 450 0

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Using the following parameters to generate figure (3.5)

m f l0 r (0) r (0) (0) (0)

5kg 1 Hz 1 m 2 m 0 550 0

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4 Discussion of results

When the spring is made very stiff, then the change of the pendulum length can be seen fromthe figure 3.3 result to be very small. This is the same result as a normal pendulum will have.This is also verified by figure 3.2 which shows a simple harmonic motion as shown in figure

3.2 (pendulum angle vs. time).When the spring stiffness is reduced (f= 1Hz), then we can see that the motion is no

longer a simple harmonic motion as can be seen in figure (3.3 and 3.4). Changing the lengthof the initial pendulum also resulted is completely different profile of the motion.

5 Appendix

5.1 Source code

1 function varargout = eme_121_lab1(varargin)

2 % EME_121_LAB1 Mfile for eme_121_lab1.fig

3 % EME_121_LAB1, by itself, creates a new EME_121_LAB1 or raises the existing

4 % singleton*.

5 %

6 % H = EME_121_LAB1 returns the handle to a new EME_121_LAB1 or the handle to

7 % the existing singleton*.

8 %

9 % EME_121_LAB1('CALLBACK',hObject,eventData,handles,...) calls the local

10 % function named CALLBACK in EME_121_LAB1.M with the given input arguments.

11 %

12 % EME_121_LAB1('Property','Value',...) creates a new EME_121_LAB1 or raises

13

% existing singleton*. Starting from the left, property value pairs are14 % applied to the GUI before eme_121_lab1_OpeningFcn gets called. An

15 % unrecognized property name or invalid value makes property application

16 % stop. All inputs are passed to eme_121_lab1_OpeningFcn via varargin.

17 %

18 % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one

19 % instance to run (singleton)".

20 %

21 % See also: GUIDE, GUIDATA, GUIHANDLES

22

23 % Edit the above text to modify the response to help eme_121_lab1

24

25 % Last Modified by GUIDE v2.5 10Apr2011 23:32:56

26

27 % By Nasser M. Abbasi

28

29 % Begin initialization code DO NOT EDIT

30 gui_Singleton = 1;

31 gui_State = struct('gui_Name', mfilename, ...

32 'gui_Singleton', gui_Singleton, ...

33 'gui_OpeningFcn', @eme_121_lab1_OpeningFcn, ...

34 'gui_OutputFcn', @eme_121_lab1_OutputFcn, ...

35 'gui_LayoutFcn', [] , ...

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36 'gui_Callback', []);

37 if nargin && ischar(varargin{1})

38 gui_State.gui_Callback = str2func(varargin{1});

39 end

40

41 if nargout

42 [varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});43 else

44 gui_mainfcn(gui_State, varargin{:});

45 end

46 % End initialization code DO NOT EDIT

47

48

49 % Executes just before eme_121_lab1 is made visible.

50 function eme_121_lab1_OpeningFcn(hObject, eventdata, handles, varargin)

51 % This function has no output args, see OutputFcn.

52 % hObject handle to figure

53 % eventdata reserved to be defined in a future version of MATLAB

54 % handles structure with handles and user data (see GUIDATA)

55 % varargin command line arguments to eme_121_lab1 (see VARARGIN)56

57 % Choose default command line output for eme_121_lab1

58 handles.output = hObject;

59

60 set(handles.figure1, 'UserData',[]);

61 set(handles.figure1,'Name','EME 121 first lab by Nasser M. Abbasi');

62

63 data.stop = false;

64 set(handles.figure1, 'UserData',data);

65

66 % Update handles structure

67 guidata(hObject, handles);

68

69 % UIWAIT makes eme_121_lab1 wait for user response (see UIRESUME)

70 % uiwait(handles.figure1);

71

72

73 % Outputs from this function are returned to the command line.

74 function varargout = eme_121_lab1_OutputFcn(hObject, eventdata, handles)

75 % varargout cell array for returning output args (see VARARGOUT);

76 % hObject handle to figure



79

80 % Get default command line output from handles structure

81 varargout{1} = handles.output;

82

83

84

85 function mass_tag_Callback(hObject, eventdata, handles)

86 % hObject handle to mass_tag (see GCBO)



89

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90 % Hints: get(hObject,'String') returns contents of mass_tag as text

91 % str2double(get(hObject,'String')) returns contents of mass_tag as a doub

92

93

94 % Executes during object creation, after setting all properties.

95 function mass_tag_CreateFcn(hObject, eventdata, handles)

96 % hObject handle to mass_tag (see GCBO)97 % eventdata reserved to be defined in a future version of MATLAB

98 % handles empty handles not created until after all CreateFcns called

99

100 % Hint: edit controls usually have a white background on Windows.

101 % See ISPC and COMPUTER.

102 if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgrou

103 set(hObject,'BackgroundColor','white');

104 end

105

106

107

108 function f_tag_Callback(hObject, eventdata, handles)

109 % hObject handle to f_tag (see GCBO)110 % eventdata reserved to be defined in a future version of MATLAB


112

113 % Hints: get(hObject,'String') returns contents of f_tag as text

114 % str2double(get(hObject,'String')) returns contents of f_tag as a double

115

116


118 function f_tag_CreateFcn(hObject, eventdata, handles)

119 % hObject handle to f_tag (see GCBO)



122





127 end

128

129

130

131 function length_tag_Callback(hObject, eventdata, handles)

132 % hObject handle to length_tag (see GCBO)



135

136 % Hints: get(hObject,'String') returns contents of length_tag as text

137 % str2double(get(hObject,'String')) returns contents of length_tag as a dou

138

139


141 function length_tag_CreateFcn(hObject, eventdata, handles)

142 % hObject handle to length_tag (see GCBO)


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145





150 end151

152

153 function angle_zero_tag_Callback(hObject, eventdata, handles)

154 % hObject handle to angle_zero_tag (see GCBO)



157

158 % Hints: get(hObject,'String') returns contents of angle_zero_tag as text

159 % str2double(get(hObject,'String')) returns contents of angle_zero_tag as a

160

161


163 function angle_zero_tag_CreateFcn(hObject, eventdata, handles)164 % hObject handle to angle_zero_tag (see GCBO)



167





172 end

173

174 function angle_speed_zero_Callback(hObject, eventdata, handles)

175 % hObject handle to angle_speed_zero (see GCBO)



178

179 % Hints: get(hObject,'String') returns contents of angle_speed_zero as text

180 % str2double(get(hObject,'String')) returns contents of angle_speed_zero a

181

182


184 function angle_speed_zero_CreateFcn(hObject, eventdata, handles)

185 % hObject handle to angle_speed_zero (see GCBO)



188





193 end

194

195 function r_zero_tag_Callback(hObject, eventdata, handles)

196 % hObject handle to r_zero_tag (see GCBO)


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199

200 % Hints: get(hObject,'String') returns contents of r_zero_tag as text

201 % str2double(get(hObject,'String')) returns contents of r_zero_tag as a dou

202

203

204 % Executes during object creation, after setting all properties.205 function r_zero_tag_CreateFcn(hObject, eventdata, handles)

206 % hObject handle to r_zero_tag (see GCBO)



209





214 end

215

216

217

218 function r_speed_zero_Callback(hObject, eventdata, handles)

219 % hObject handle to r_speed_zero (see GCBO)



222

223 % Hints: get(hObject,'String') returns contents of r_speed_zero as text

224 % str2double(get(hObject,'String')) returns contents of r_speed_zero as a d

225

226


228 function r_speed_zero_CreateFcn(hObject, eventdata, handles)

229 % hObject handle to r_speed_zero (see GCBO)



232





237 end

238

239

240 % Executes on button press in run_btn.

241 function run_btn_Callback(hObject, eventdata, handles)

242 % hObject handle to run_btn (see GCBO)



245

246 [data,status] = parse_input(handles);

247 if not(status)

248 return;

249 end

250

251 data.handles = handles;

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252 data.g = 9.8;

253

254 enable_all(handles,'off');

255 userData = get(handles.figure1, 'UserData');

256 userData.stop = false;

257 set(handles.figure1, 'UserData',userData);

258

259 [g_msg,g_status]=process_eme_121_lab1(data);

260 if not(g_status)

261 uiwait(errordlg(sprintf('Processing terminated: %s',g_msg),...

262 'Bad Input', 'modal'));

263 uicontrol(handles.f_tag);

264 end

265 enable_all(handles,'on');

266

267 %

268 function [data,status]= parse_input(handles)

269

270 [data.mass,status]=verify_valid_positive_numeric...

271 (get(handles.mass_tag,'String'),handles.mass_tag,...272 'Mass must be positive number');

273 if not(status)

274 return;

275 end

276

277 [data.f,status]=verify_valid_positive_numeric...

278 (get(handles.f_tag,'String'),handles.f_tag,...

279 'natural frequency must be positive number');

280 if not(status)

281 return;

282 end

283

284

285 [data.L,status]=verify_valid_positive_numeric...

286 (get(handles.length_tag,'String'),handles.length_tag,...

287 'pendulum length must be positive number');

288 if not(status)

289 return;

290 end

291

292 [data.angle_zero,status]=verify_valid_numeric...

293 (get(handles.angle_zero_tag,'String'),handles.angle_zero_tag,...

294 'Initial angle must be numerical value');

295 if not(status)

296 return;

297 end

298

299 if abs(data.angle_zero)>180

300 uiwait(errordlg('Initial angle must be between 0 and 180 degrees only',...

301 'Bad Input', 'modal'));

302 status = 0;

303 uicontrol(handles.angle_zero);

304 return

305 else

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306 data.angle_zero = data.angle_zero*pi/180;

307 end

308

309 [data.r_zero,status]=verify_valid_positive_numeric...

310 (get(handles.r_zero_tag,'String'),handles.r_zero_tag,...

311 'initial r must be numerical value');

312 if not(status)313 return;

314 end

315

316

317 [data.r_speed_zero,status]=verify_valid_numeric...

318 (get(handles.r_speed_zero,'String'),handles.r_speed_zero,...

319 'initial r speed must be numerical value');

320 if not(status)

321 return;

322 end

323

324

325 [data.time_step,status]=verify_valid_numeric...326 (get(handles.time_Step_tag,'String'),handles.time_Step_tag,...

327 'time step must be zero or larger');

328 if not(status)

329 return;

330 end

331

332 [data.angle_speed_zero,status]=verify_valid_numeric...

333 (get(handles.angle_speed_zero,'String'),handles.angle_speed_zero,...

334 'initial angle speed must be numerical value');

335 if not(status)

336 return;

337 end

338

339 [data.max_t,status]=verify_valid_positive_numeric...

340 (get(handles.max_t_tag,'String'),handles.max_t_tag,...

341 'maximum simulation time must be positive number');

342 if not(status)

343 return;

344 end

345

346 contents = cellstr(get(handles.ode_solver_tag,'String'));

347 data.solver = contents{get(handles.ode_solver_tag,'Value')};

348

349

350 data.k = data.mass*

(2*

pi*

data.f)^2;

351

352 %

353 function enable_all(handles,to)

354 set(handles.mass_tag,'Enable',to);

355 set(handles.f_tag,'Enable',to);

356 set(handles.length_tag,'Enable',to);

357 set(handles.angle_zero_tag,'Enable',to);

358 set(handles.r_speed_zero,'Enable',to);

359 set(handles.angle_speed_zero,'Enable',to);

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360 set(handles.r_zero_tag,'Enable',to);

361 set(handles.max_t_tag,'Enable',to);

362 set(handles.ode_solver_tag,'Enable',to);

363 set(handles.time_Step_tag,'Enable',to);

364

365 function max_t_tag_Callback(hObject, eventdata, handles)

366 % hObject handle to max_t_tag (see GCBO)367 % eventdata reserved to be defined in a future version of MATLAB


369

370 % Hints: get(hObject,'String') returns contents of max_t_tag as text

371 % str2double(get(hObject,'String')) returns contents of max_t_tag as a doub

372

373


375 function max_t_tag_CreateFcn(hObject, eventdata, handles)

376 % hObject handle to max_t_tag (see GCBO)



379





384 end

385

386

387 % Executes on button press in reset_tag.

388 function reset_tag_Callback(hObject, eventdata, handles)

389 % hObject handle to reset_tag (see GCBO)



392

393

394 data = get(handles.figure1, 'UserData');

395 data.stop = true;

396 set(handles.figure1, 'UserData',data);

397 enable_all(handles,'on');

398

399

400 % Executes on selection change in ode_solver_tag.

401 function ode_solver_tag_Callback(hObject, eventdata, handles)

402 % hObject handle to ode_solver_tag (see GCBO)



405

406 % Hints: contents = cellstr(get(hObject,'String')) returns ode_solver_tag content

407 % contents{get(hObject,'Value')} returns selected item from ode_solver_tag

408


410 function ode_solver_tag_CreateFcn(hObject, eventdata, handles)

411 % hObject handle to ode_solver_tag (see GCBO)



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414

415 % Hint: popupmenu controls usually have a white background on Windows.




419 end

420

421 function time_Step_tag_Callback(hObject, eventdata, handles)

422 % hObject handle to time_Step_tag (see GCBO)



425

426 % Hints: get(hObject,'String') returns contents of time_Step_tag as text

427 % str2double(get(hObject,'String')) returns contents of time_Step_tag as a

428

429


431 function time_Step_tag_CreateFcn(hObject, eventdata, handles)

432 % hObject handle to time_Step_tag (see GCBO)

433 % eventdata reserved to be defined in a future version of MATLAB434 % handles empty handles not created until after all CreateFcns called

435





440 end

1 function [g_msg,g_status]=process_eme_121_lab1(data)

2 % This function is called by the Matlab GUI to solve

3 % the equation of motion for Lab 1 problem, EME 121,4 % spring 2011, UC Davis.

5 %

6 % INPUT: data, a record which contains the problem parameters

7 %

8 % The function will call ode45 solver and plot the solution

9 %

10 % by Nasser M. Abbasi

11 % 4/12/2011

12

13

14 % Reset axes for plotting

15 cla(data.handles.axes,'reset');

16 cla(data.handles.time_angle_axes,'reset');

17 cla(data.handles.time_r_axes,'reset');

18 cla(data.handles.angle_r_axes,'reset');

19

20 %Check if using auto step size of an explicit step size. see

21 %GUI for input choice.

22 if data.time_step==0

23 time_span=[0 data.max_t];

24 else

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25 time_span=0:data.time_step/1000:data.max_t;

26 end

27

28 %set the yaxis for plotting

29 max_y = data.L;

30

31 %set the initial conditions for ode4532 IC = [data.r_zero;data.r_speed_zero;data.angle_zero;data.angle_speed_zero];

33 options = odeset('OutputFcn',@output);

34

35 g_status = true;

36 g_msg='';

37

38 %call the solver

39 [t,x] = feval(data.solver,@rhs,time_span,IC,options,data);

40

41

42 %plot the result

43 N=length(t);

44 picks=1:N;45

46 set(data.handles.figure1, 'CurrentAxes',data.handles.time_angle_axes);

47 angle=x(:,3);

48 plot(t(picks),angle(picks)*180/pi,'');

49 title('pendulum angle vs time');

50 xlabel('Time (sec)');

51 ylabel('angle (degree)');

52 grid;

53 drawnow;

54

55 set(data.handles.figure1, 'CurrentAxes',data.handles.time_r_axes);

56 r=x(:,1);

57 stairs(t(picks),r(picks),'');

58 title('pendulum length vs time');

59 xlabel('Time (sec)'); ylabel('length (m)');

60 grid;

61 drawnow;

62

63 set(data.handles.figure1, 'CurrentAxes',data.handles.angle_r_axes);

64

65 plot(angle(picks)*180/pi,r(picks),'');

66 title('pendulum angle vs length');

67 xlabel('Angle (degree)'); ylabel('length (m)');

68 grid;

69 drawnow;

70

71

72 %

73 %

74 %

75 function dx=rhs(,x,data)

76 %the ode45 function

77 temp = x(1)data.L;

78

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79 if abs(tempmax_y

91 max_y = x(1)+0.2*x(1);

92 end

93 end

94

95 %

96 %

97 %

98 function status= output(t,x,,data)99 %called by ode45 after each step. Plot the current

100 %pendulum position for simulation

101

102 userData = get(data.handles.figure1, 'UserData');

103 if userData.stop

104 status=true;

105 g_status =true;

106 else

107 status = false;

108 if not(isempty(t))

109 plot_solution(x(1,end),x(3,end),t(1),data);

110 %pause(0.1);

111 if x(1,end)>10*data.L %spring stretched too far

112 status = true;

113 g_status = false;

114 g_msg ='spring over stretched';

115 end

116 end

117 end

118 end

119

120 %

121 %

122 %

123 function plot_solution(r,theta,t,data)

124 %plot the final solution

125 set(0,'CurrentFigure',data.handles.figure1);

126 set(data.handles.figure1, 'CurrentAxes',data.handles.axes);

127

128 [x_local,y] = pol2cart(thetapi/2,r);

129 plot(x_local,y,'o','MarkerSize',20,'MarkerEdgeColor','r',...

130 'MarkerFaceColor','r','LineWidth',2);

131 [x_local,y] = nma_spring.make(r,theta(pi/2),30);

132 hold on;

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133 line(x_local,y);

134 plot(0,0,'o','MarkerSize',5,'MarkerEdgeColor','k',...

135 'MarkerFaceColor','k','LineWidth',1);

136 title(sprintf(...

137 'time = %3.4f, angle(degree) = %3.3f, r = %3.3f, k=%3.4f',...

138 t,theta*180/pi,r,data.k));

139

140 xlim([max_y max_y]);

141 ylim([max_y max_y]);

142 %refreshdata

143 grid;

144 drawnow;

145 hold off;

146 end

147

148 end

1 classdef nma_spring2 %

3 %static class to make spring for plotting animations

4 %by Nasser M. Abbasi

5

6

7 properties

8 end

9

10 methods(Static)

11

12 %

13 %

14 %15 function [x,y] = make(r,theta,N)

16 %r: total length of spring

17 %theta: in radians, anticlock wise is positive,

18 % theta zero is position xaxis

19 %N: number of twists in spring

20 %

21 %OUTPUT:

22 % x,y coordinates of line to use to plot spring

23 len = (4/6)*r;

24 p = zeros(N,2);

25 delr = len/N;

26

27 r0 = (1/6)*r;

28 p(2,1) = r0;

29 p(2,2) = theta;

30

31 for n=3:N2

32 p(n,1)=r0+delr*n;

33 z=atan(2*delr/p(n,1));

34 p(n,2)=theta+(1)^n*z;

35 end

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36 p(end1,1)=(5/6)*r; p(end1,2)=theta;

37 p(end,1)=r; p(end,2)=theta;

38

39 [x,y] = pol2cart(p(:,2),p(:,1));

40 end

41

42 %43 function [x,y] = makeBox(w,h)

44 x = zeros(5,1);

45 y = zeros(5,1);

46 x(1)= w/2; y(1)=0;

47 x(2)= w/2; y(2)=h/2;

48 x(3)= w/2; y(3)=h/2;

49 x(4)=w/2; y(4)=0;

50 x(5)=x(1); y(5)=y(1);

51

52 end

53 %

54 %

55 %

56 function [x,y] = makeV2(len,N,w)

57 %len: total length of spring

58 %N: number of twists in spring

59 %

60 %OUTPUT:

61 % x,y coordinates of line to use to plot spring

62

63 nCoordinates = 2*N+4;

64 p = zeros(nCoordinates,2);

65 h = (1/6)*len;

66 del=(len2*h)/(N+1);

67 done = false;

68 n = 1;

69 while not(done)

70

71 if n==1

72 p(1,1)=0;

73 p(1,2)=0;

74 n = n + 1;

75 elseif n==2

76 p(2,1)=0;

77 p(2,2)=h;

78 n = n + 1;

79 elseif n


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90 else

91 p(n,1) = 0;

92 p(n,2)=p(n1,2)+h;

93 done = true;

94 end

95 end

96 x=p(:,1);97 y=p(:,2);

98

99 end

100

101

102

103 %

104 %

105 %

106 function test(theta)

107

108 close all;

109

110 theta = theta*pi/180;

111 figure;

112 set(gcf,'Units','normalized');

113 delr=0.3;

114 for r=1:.1:3

115 cla;

116 [x,y] = nma_spring.make(r,theta,30);

117 line(x,y);

118 hold on;

119

120 %baseX = [2*delr*cos((pi/2)theta) 2*delr*sin(theta)];

121 %baseY = [2*delr*sin((pi/2)theta) 2*delr*cos(theta)];

122

123 baseX = [2*delr*sin(abs(theta)) 2*delr*sin(abs(theta))];

124 baseY = [2*delr*cos(theta) 2*delr*cos(theta)];

125 line(baseX,baseY);

126

127 triX=[baseX(1) ...

128 baseX(1) ...

129 30*delr*cos(theta)abs(baseX(1))...

130 baseX(1)];

131

132 triY=[baseY(1) ...

133 (30*delr*sin(abs(theta))+abs(baseY(1)))...

134 (30*

delr*

sin(abs(theta))+abs(baseY(1)))...

135 baseY(1)];

136

137 line(triX,triY);

138

139 L=sqrt(x(end)^2+y(end)^2);

140 xx0=L*cos(theta);

141 yy0=L*sin(abs(theta));

142 massX=[xx0 ...

143 xx0+2*delr*sin(abs(theta)) ...

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144 xx0+2*delr*sin(abs(theta))+4*delr*cos(theta) ...

145 xx0+2*delr*sin(abs(theta))+4*delr*cos(theta)4*delr*sin(abs(th


147 xx0];

148

149 massY=[ yy0 ...

150 yy0+2*delr*cos(theta) ...151 yy0+2*delr*cos(theta)4*delr*sin(abs(theta)) ...

152 yy0+2*delr*cos(theta)4*delr*sin(abs(theta))4*delr*cos(theta


154 yy0];

155

156 line(massX,massY);

157

158 xlim([3,10]); ylim([10,3]);

159

160 set(gca,'DataAspectRatioMode','manual','DataAspectRatio',[1 1 1])

161 drawnow;

162 pause(.1);

163 end164

165 end

166

167 %

168 %

169 %

170 function testV2(len)

171

172 close all;

173

174 theta = 0;

175 figure;

176 set(gcf,'Units','normalized');

177 delr=0.3;

178 for r=1:len/3:len

179 cla;

180 [x,y] = nma_spring.makeV2(r,10,1);

181 line(x,y);

182 hold on;

183

184 %baseX = [2*delr*cos((pi/2)theta) 2*delr*sin(theta)];

185 %baseY = [2*delr*sin((pi/2)theta) 2*delr*cos(theta)];

186

187 baseX = [2*delr*sin(abs(theta)) 2*delr*sin(abs(theta))];

188 baseY = [2*

delr*

cos(theta) 2*

delr*

cos(theta)];

189 line(baseX,baseY);

190

191 triX=[baseX(1) ...

192 baseX(1) ...

193 30*delr*cos(theta)abs(baseX(1))...

194 baseX(1)];

195

196 triY=[baseY(1) ...


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199 baseY(1)];

200

201 line(triX,triY);

202

203 L=sqrt(x(end)^2+y(end)^2);

204 xx0=L*cos(theta);205 yy0=L*sin(abs(theta));

206 massX=[xx0 ...

207 xx0+2*delr*sin(abs(theta)) ...

208 xx0+2*delr*sin(abs(theta))+4*delr*cos(theta) ...



211 xx0];

212

213 massY=[ yy0 ...

214 yy0+2*delr*cos(theta) ...

215 yy0+2*delr*cos(theta)4*delr*sin(abs(theta)) ...


217 yy0+2*delr*cos(theta)4*delr*sin(abs(theta))4*delr*cos(theta218 yy0];

219

220 line(massX,massY);

221

222 xlim([3,10]); ylim([10,3]);

223

224 set(gca,'DataAspectRatioMode','manual','DataAspectRatio',[1 1 1])

225 drawnow;

226 pause(.3);

227 end

228

229 end

230

231 end

232 end

About Pushbutton Stop

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