Math Problem Statement

% Parameters

m1 = 1; % Mass of the underwater body

m2 = 0.5; % Displaced water equivalent mass

K = 0.1; % Drag coefficient

g = 9.81; % Gravitational acceleration

% Equilibrium values (linearization point)

x1_e = 0;

x2_e = 0;

x3_e = 2 * pi; % Equilibrium angle (multiple of pi)

% State-space matrices A and B (computed manually or symbolically)

A = [0 1 0;

 0 -K/m1  -(m2 - m1) * g / m1;

 0 0 0];

B = [0;

 1/m1;

 0];

% Define state-space model

sys = ss(A, B, eye(3), 0);

% Display the state-space model

disp('State-space model:');

disp(sys);

Solution

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Control Theory
State-Space Representation

Formulas

State-space representation: x' = Ax + Bu

Theorems

Eigenvalue stability criteria

Suitable Grade Level

Undergraduate