(i) Separation of uariables for 2\'d-order ODEs? Separation of variables is usef
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(i) Separation of uariables for 2'd-order ODEs? Separation of variables is useful for solving 1st-order ODEs. Is it possible to find an analytical solution for y(t) for the 2nd-order ODE 2 di to the right via separation of variables. Yes/No. d2 dt2 Explain: 2.16 Numerical solution of ordinary differential equations. The equations of motion for the system described in Section 3.1 are 2 (508.89 sin(gsin(B) coslge) daiB 21.556+sin B) =-sin(4B) cos(4B) qa (a) Classify the previous set of equations by picking the relevant qualifiers from the list below Uncoupled Linear Homogeneous Constant-coefficient 1"-order Algebraic Coupled Nonlinear Inhomogeneous Variable-coefficient 2nd-order Differential t 10. Use qa(0) = 1.00 and two different initial values of q, namiely qa(0-45° and qa(0) = 90°. Submit a printed copy of your MotionGenesis or M AT LAB ® file. Hint: LLeMuluntieneuseun-an sine! Solve ODE. Result: (b) Optional: Find the maximum absolute value of qa(t) for 0 . Maximum absolute value of qB(t) when q4(0-45% Maximum absolute value of qa(t) when qA(0-90°. qa(t=1.66) qa(t=8.18) = ·Explanation / Answer
clear all;
% Define a symbolic variable here qa nad qb
syms qa(t) qb(t)
% S1'' = -k * sqrt( S1'^2 + S2'^2 ) * S1',
% S2'' = -k * sqrt( S1'^2 + S2'^2 ) * S2' - g.
EqS1 = diff(qa,2) == 2*(508.89*sin(qa)-sin(qa)*diff(qa)*diff(qb));
EqS2 = diff(qb,2) == -sin(qb)*cos(qb)*diff(qa^2);
% now convert the symbolic equations to 4 first order differential
% equations.
[ODE,Vars] = odeToVectorField(EqS1, EqS2)
% this converts the problem which into a system which is recognisable by
% ode45 to solve the problem with given initial conditions
sys=matlabFunction(ODE,'vars', {'t','Y'})
% To solve this system, call the MATLAB ode45 numerical solver using the
% generated MATLAB function as an input
tspan=0:0.1:10; % time span
% initial conditions
qa1=45;
qa2=90;
qb0=1;
% initial condition matrix
inc1=[1 0 45 0]; % for [qb qb_dot qa qa_dot]
inc2=[1 0 90 0];
% Solving the ode with ode45 function
sol = ode45(sys,tspan,inc1);
% Plot the Solution
% Plot the solution using linspace to generate 100 points in the interval [0,10]
% and deval to evaluate the solution for each point.
fplot(@(Y)deval(sol,Y,1), [0, 10]);
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above is the matlab code, you can change the deval(sol,Y,<1 or 2 or 3 or 4>). to plot qb or qb_dot or qa or qa_dot respectively and the value at any point from the plotted graph itself.
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