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 February 29th, 2016, 11:16 AM #1 Newbie   Joined: Feb 2016 From: singapore Posts: 1 Thanks: 0 Runge kutta help! how do i use runge kutta on a 2nd order equations? M(d2x/dt2)=Fn(sin θ - uCos θ ) M(d2z/dt2)=Fn(cos θ + uSin θ ) - Mg﻿ i tried Mzdoubledot as shown in the code below, however i dont know how to combine Mzdoubledot with Mxdoubledot. Fn,M,θ,u is constant fn/M = 0.866 clc; % Clears the screen clear all; thete=30; g=9.81; %Constant h=0.1; % step size tfinal = 3; N=ceil(tfinal/h); %y = zeros(1,length(x)); t(1) = 0; % initial condition y(1) = 5; F_zy = @(t,thete) 0.866*(cos(thete)+0.5774*(sin(thete)))-g; F_xy = @(t,thete) 0.866*(sin(thete)-0.5774*(cos(thete))); for i=1:N % calculation loop %update time t(i+1)=t(i)+h; %update motions k_1 = F_xy(t(i),y(i)); k_2 = F_xy(t(i)+0.5*h,y(i)+0.5*h*k_1); k_3 = F_xy((t(i)+0.5*h),(y(i)+0.5*h*k_2)); k_4 = F_xy((t(i)+h),(y(i)+k_3*h)); k_11 = F_zy(t(i),y(i)); k_22 = F_zy(t(i)+0.5*h,y(i)+0.5*h*k_11); k_33 = F_zy((t(i)+0.5*h),(y(i)+0.5*h*k_22)); k_44 = F_zy((t(i)+h),(y(i)+k_33*h)); y(i+1) = y(i) + (1/6)*(k_1+2*k_2+2*k_3+k_4)*h; y(i+1) = y(i) + (1/6)*(k_11+2*k_22+2*k_33+k_44)*h;% main equation end hold on plot(t,y,'+-', 'Linewidth', 1.5, 'color', 'blue') xlabel('time') ylabel('height') legend('RK4')﻿ Tags kutta, runge, runge-kutta Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post praveengummadi35 Calculus 0 March 27th, 2014 05:58 PM 0nad Applied Math 1 October 2nd, 2012 10:20 AM thunderkasi Real Analysis 1 October 25th, 2011 04:15 AM UlrichRekenin Calculus 0 August 22nd, 2011 10:54 AM mathmoron Math Software 1 April 8th, 2010 06:35 AM

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