How to stop falling cube?

Hi everyone,

I simulated a free falling cube (the code is provided as below). I want to stop falling as the lowest vertex reaches to ground. Could you please help me to do that? thanks

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clear all;clc;close all;

%% Geomtry

%%

% Define the size of the cube and the radius of the balls

cube_size = 1; % size of the cube

ball_radius = 0.15; % radius of the balls

R=cube_size/2;% distance of origin of cube from the verticies

Size_of_View=2; % view of the the results

%% Dynamic parameters

g=10; % gravity

v0=0;% initial velocity

z0=3;% initial position in space

FinalTime=1;% Time priod

time = linspace(0, FinalTime, 50);

z_Falling=-0.5*g*time.^2+v0*time+z0;

%% Solving the equation of motion

for i=1:length(time)

% Create the vertices of the cube

clf;

%% Rotation

Angle_Rotation_X=-0.2;

Angle_Rotation_Y=0.3;

Angle_Rotation_Z=0;

eul = [Angle_Rotation_X Angle_Rotation_Y Angle_Rotation_Z];

rotmXYZ = eul2rotm(eul,'XYZ');

%% Creating Dynamic Cube

vertices = [-R -R -R;

R -R -R;

R R -R;

-R R -R;

-R -R R;

R -R R;

R R R;

-R R R;]*rotmXYZ;

vertices(:,3)=vertices(:,3)+z_Falling(i);

%% Create the faces of the cube

faces = [1 2 3 4;

2 6 7 3;

6 5 8 7;

5 1 4 8;

1 2 6 5;

4 3 7 8];

%% Plot the cube

patch('Vertices', vertices, 'Faces', faces, 'FaceColor', 'b', 'EdgeColor', 'k');

view([30 35])

% Create the balls at each vertex

hold on;

for j = 1:size(vertices, 1)

[x, y, z] = sphere;

x = x * ball_radius + vertices(j, 1);

y = y * ball_radius + vertices(j, 2);

z = z * ball_radius + vertices(j, 3);

surf(x, y, z, 'FaceColor', 'r', 'EdgeColor', 'none');

view([30 35])

end

%% Refrence Plane

vertices_Ref_Plane=[-Size_of_View -Size_of_View 0;

cube_size + Size_of_View -Size_of_View 0;

cube_size + Size_of_View cube_size + Size_of_View 0;

-Size_of_View cube_size + Size_of_View 0;];

faces_Plane = [1 2 3 4];

patch('Vertices', vertices_Ref_Plane, 'Faces',faces_Plane, 'FaceColor', 'c', 'EdgeColor', 'k');

%% Set axis limits

SV=Size_of_View;

xlim([- Size_of_View, cube_size + Size_of_View]);

ylim([- Size_of_View, cube_size + Size_of_View]);

zlim([0, cube_size + Size_of_View]);

% Set axis labels

xlabel('X');

ylabel('Y');

zlabel('Z');

grid on

drawnow

view(3);

view([-70 30])

end

Answer 1

[Sulaymon Eshkabilov]

Here is the corrected code to halt the cube at the ground:

% Define the size of the cube and the radius of the balls
cube_size = 1; % size of the cube
ball_radius = 0.15; % radius of the balls
R=cube_size/2;% distance of origin of cube from the verticies
Size_of_View=2; % view of the the results
%% Dynamic parameters
g=10; % gravity
v0=0;% initial velocity
z0=3;% initial position in space
FinalTime=1;% Time priod
time = linspace(0, FinalTime, 75);
z_Falling=-0.5*g*time.^2+v0*time+z0;
IDX = (z_Falling>0.6);                % Approximately when the cube edge hits the ground
time = time(IDX);
z_Falling = z_Falling(IDX);
%% Solving the equation of motion

for i=1:length(time)
    % Create the vertices of the cube
    clf;
    %Rotation
    Angle_Rotation_X=-0.2;
    Angle_Rotation_Y=0.3;
    Angle_Rotation_Z=0;
    eul = [Angle_Rotation_X Angle_Rotation_Y Angle_Rotation_Z];
    rotmXYZ = eul2rotm(eul,'XYZ');
   % Creating Dynamic Cube
    vertices = [-R -R -R;
        R -R -R;
        R R -R;
        -R R -R;
        -R -R  R;
        R -R R;
        R R R;
        -R R R;]*rotmXYZ;
    
  vertices(:,3)=vertices(:,3)+z_Falling(i);

    %Create the faces of the cube
    faces = [1 2 3 4;
        2 6 7 3;
        6 5 8 7;
        5 1 4 8;
        1 2 6 5;
        4 3 7 8];
    % Plot the cube
    patch('Vertices', vertices, 'Faces', faces, 'FaceColor', 'b', 'EdgeColor', 'k');
    view([30 35])
    % Create the balls at each vertex
    hold on;
    for j = 1:size(vertices, 1)
        [x, y, z] = sphere;
        x = x * ball_radius + vertices(j, 1);
        y = y * ball_radius + vertices(j, 2);
        z = z * ball_radius + vertices(j, 3);
        surf(x, y, z, 'FaceColor', 'r', 'EdgeColor', 'none');
        view([30 35])
    end
    % Refrence Plane
    vertices_Ref_Plane=[-Size_of_View -Size_of_View 0;
        cube_size +  Size_of_View -Size_of_View 0;
        cube_size +  Size_of_View cube_size +  Size_of_View 0;
        -Size_of_View cube_size +  Size_of_View 0;];
    faces_Plane = [1 2 3 4];
    patch('Vertices', vertices_Ref_Plane, 'Faces',faces_Plane, 'FaceColor', 'c', 'EdgeColor', 'k');
    
    % Set axis limits
    SV=Size_of_View;
    xlim([- Size_of_View, cube_size +  Size_of_View]);
    ylim([- Size_of_View, cube_size +  Size_of_View]);
    zlim([0, cube_size +  Size_of_View]);
    
    % Set axis labels
    xlabel('X');
    ylabel('Y');
    zlabel('Z');
    
    grid on
    drawnow
    view(3);
    view([-70 30])
end

[N/A]

Thanks, it works

[Sulaymon Eshkabilov]

Most welcome! Glad to help.

[N/A]

Just one thing remained... I entered the part you programmed inside the loop. I want to stop loop as it reaches to the ground. However, I programmed as you can see lines from 43 to 47. However, it is not the optimized way to save memory. Could you please suggest me a better way for stopping the loop after the ball reaches to the ground? I pasted the code again in following. Thanks,

% Define the size of the cube and the radius of the balls

cube_size = 1; % size of the cube

ball_radius = 0.15; % radius of the balls

R=cube_size/2;% distance of origin of cube from the verticies

Size_of_View=2; % view of the the results

%% Dynamic parameters

g=10; % gravity

v0=0;% initial velocity

z0=3;% initial position in space

FinalTime=1;% Time priod

time_step=75;

time = linspace(0, FinalTime, time_step);

z_Falling=-0.5*g*time.^2+v0*time+z0;

Angle_Rotation_X=-0.5;

Angle_Rotation_Y=-0.2;

Angle_Rotation_Z=0.0;

eul = [Angle_Rotation_X Angle_Rotation_Y Angle_Rotation_Z];

rotmXYZ = eul2rotm(eul,'XYZ');

%% Solving the equation of motion

for i=1:length(time)

% Create the vertices of the cube

clf;

%Rotation

% Creating Dynamic Cube

vertices = [-R -R -R;

R -R -R;

R R -R;

-R R -R;

-R -R R;

R -R R;

R R R;

-R R R;]*rotmXYZ;

IDX = (min(vertices(:,3))+z_Falling-ball_radius>0); % Approximately when the cube edge hits the ground

time = time(IDX);

z_Falling = z_Falling(IDX);

z_Falling(end) % Can you please refine these followign 5 lines for the code here for saving memory?

if i>=length(IDX)

z_Falling(i)= z_Falling(end);

time(i)=0;

end

vertices(:,3)=vertices(:,3)+z_Falling(i);

%%

%Create the faces of the cube

faces = [1 2 3 4;

2 6 7 3;

6 5 8 7;

5 1 4 8;

1 2 6 5;

4 3 7 8];

% Plot the cube

patch('Vertices', vertices, 'Faces', faces, 'FaceColor', 'b', 'EdgeColor', 'k');

view([30 35])

% Create the balls at each vertex

hold on;

for j = 1:size(vertices, 1)

[x, y, z] = sphere;

x = x * ball_radius + vertices(j, 1);

y = y * ball_radius + vertices(j, 2);

z = z * ball_radius + vertices(j, 3);

surf(x, y, z, 'FaceColor', 'r', 'EdgeColor', 'none');

view([30 35])

end

% Refrence Plane

vertices_Ref_Plane=[-Size_of_View -Size_of_View 0;

cube_size + Size_of_View -Size_of_View 0;

cube_size + Size_of_View cube_size + Size_of_View 0;

-Size_of_View cube_size + Size_of_View 0;];

faces_Plane = [1 2 3 4];

patch('Vertices', vertices_Ref_Plane, 'Faces',faces_Plane, 'FaceColor', 'c', 'EdgeColor', 'k');

% Set axis limits

SV=Size_of_View;

xlim([- Size_of_View, cube_size + Size_of_View]);

ylim([- Size_of_View, cube_size + Size_of_View]);

zlim([0, cube_size + Size_of_View]);

% Set axis labels

xlabel('X');

ylabel('Y');

zlabel('Z');

grid on

drawnow

% view(3);

% view([-70 30])

end