1.

${\displaystyle j={\frac {9\pi ^{2}v_{0}}{2\mathrm {T} ^{2}}}\cos \left({\frac {3\pi t}{\mathrm {T} }}\right)}$

${\displaystyle a={\frac {3\pi v_{0}}{2\mathrm {T} }}\sin \left({\frac {3\pi t}{\mathrm {T} }}\right)}$

${\displaystyle v={\frac {v_{0}}{2}}\left(1-\cos \left({\frac {3\pi t}{\mathrm {T} }}\right)\right)}$

${\displaystyle x={\frac {v_{0}}{2}}\left(t-{\frac {\mathrm {T} }{3\pi }}\sin \left({\frac {3\pi t}{\mathrm {T} }}\right)\right)}$

${\displaystyle a_{1}=0}$

${\displaystyle v_{1}=v_{0}}$

${\displaystyle x_{1}={\frac {v_{0}\mathrm {T} }{6}}}$

2.

${\displaystyle j=0}$

${\displaystyle a=0}$

${\displaystyle v=v_{0}}$

${\displaystyle x=v_{0}\left(t-{\frac {\mathrm {T} }{6}}\right)}$

${\displaystyle a_{2}=0}$

${\displaystyle v_{2}=v_{0}}$

${\displaystyle x_{2}={\frac {v_{0}\mathrm {T} }{2}}}$

3.

${\displaystyle j=-{\frac {9\pi ^{2}v_{0}}{2\mathrm {T} ^{2}}}\cos \left({\frac {3\pi t}{\mathrm {T} }}\right)}$

${\displaystyle a=-{\frac {3\pi v_{0}}{2\mathrm {T} }}\sin \left({\frac {3\pi t}{\mathrm {T} }}\right)}$

${\displaystyle v={\frac {v_{0}}{2}}\left(1+\cos \left({\frac {3\pi t}{\mathrm {T} }}\right)\right)}$

${\displaystyle x={\frac {v_{0}}{2}}\left(t+{\frac {\mathrm {T} }{3\pi }}\sin \left({\frac {3\pi t}{\mathrm {T} }}\right)+{\frac {\mathrm {T} }{3}}\right)}$

${\displaystyle a_{3}=0}$

${\displaystyle v_{1}=v_{0}}$

${\displaystyle x_{\mathrm {f} }={\frac {2v_{0}\mathrm {T} }{3}}}$

Max.

${\displaystyle v_{\max }=v_{0}={\frac {3x_{\mathrm {f} }}{2\mathrm {T} }}}$

${\displaystyle a_{\max }={\frac {3\pi v_{0}}{2\mathrm {T} }}={\frac {9\pi x_{\mathrm {f} }}{4\mathrm {T} ^{2}}}}$

${\displaystyle j_{\max }={\frac {9\pi ^{2}v_{0}}{2\mathrm {T} ^{2}}}={\frac {27\pi ^{2}x_{\mathrm {f} }}{4\mathrm {T} ^{3}}}}$

This media was created with Scilab, a free open-source software. Here is a listing of the Scilab source used to create this file.

function [t1, t2, t3] = indice(t)
    t1 = (t < 1/3);
    t2 = (t >= 1/3) & (t < 2/3);
    t3 = (t >= 2/3);
endfunction

function [j]=jerk(t)
    [t1, t2, t3] = indice(t);
    j = zeros(t);
    j(t1) = (9*%pi^2/2)*cos(3*%pi*t(t1));
    j(t2) = 0;
    j(t3) = -(9*%pi^2/2)*cos(3*%pi*t(t3));
endfunction

function [a]=acceleration(t)
    [t1, t2, t3] = indice(t);
    a = zeros(t);
    a(t1) = (3*%pi/2)*sin(3*%pi*t(t1));
    a(t2) = 0;
    a(t3) = -(3*%pi/2)*sin(3*%pi*t(t3));
    endfunction

function [v] = vitesse(t)
    [t1, t2, t3] = indice(t);
    v = zeros(t);
    v(t1) = (1/2)*(1 - cos(3*%pi*t(t1)));
    v(t2) = 1;
    v(t3) = (1/2)*(1 + cos(3*%pi*t(t3)));
endfunction

function [x] = position(t)
    [t1, t2, t3] = indice(t);
    x = zeros(t);
    x(t1) = (1/2)*(t(t1) - (1/3/%pi)*sin(3*%pi*t(t1)));
    x(t2) = t(t2) - 1/6;
    x(t3) = (1/2)*(t(t3) + (1/3/%pi)*sin(3*%pi*t(t3))) + 1/6;
endfunction

t = 0:0.005:1;

j = jerk(t);
a = acceleration(t);
v = vitesse(t);
x = position(t);

scf(0);
clf;

subplot(4, 1, 1)
plot(t, x)
xtitle("position", "t/T", "$x/(v_0 \mathrm{T})$")

subplot(4, 1, 2)
plot(t, v)
xtitle("vitesse", "t/T", "$v/(v_0)$")

subplot(4, 1, 3)
plot(t, a)
xtitle("accélération", "t/T", "$a\times \mathrm{T}/v_0$")

subplot(4, 1, 4)
xtitle("à-coup", "t/T", "$j \times \mathrm{T}^2/v_0$")
plot(t, j)

I, the copyright holder of this work, hereby publish it under the following licenses:

Ushbu hujjatdan nusxa ko‘chirish, tarqatish va/yoki o‘zgartirish uchun GNU Erkin guvohnoma litsenziyasi (GNU Free Documentation License), 1.2 va har qanday keyingi versiyalar shartlariga muvofiq ruxsat berilgan yoki Ochiq kodli dasturlar jamiyati (Free Software Foundation) tomonidan chop etilgan; oʻzgarmas boʻlimlarsiz, oldingi muqova matnlari va orqa muqova matnlarisiz. Litsenziya nusxasi GNU Erkin guvohnoma litsenziyasi (GNU Free Documentation License) boʻlimiga kiritilgan.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.

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