Edit detail for SandBox9 revision 2 of 2
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Editor: test1
Time: 2013/04/30 16:05:31 GMT+0 |
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| Note: | ||
removed: - Load jetbundle modules - \begin{axiom} - )lib JBC JBFC JBC- JBFC- BFC BFC- JB JBX JBLF DE SEM DIFF JBE IJB CK - \end{axiom} removed: - - :: - - jb:=IJB('t,'u,'p,2,3); - jbe:=JBE jb; - de:=DE(jb,jbe); - ck:=CK(jb,jbe); - eq1:jbe := m*P(1,[2]) + U(1)/L*U(3) - eq2:jbe := m*P(2,[2]) + U(2)/L*U(3) + m*g - eq3:jbe := U(1)^2 + U(2)^2 - L^2 - printSys [eq1,eq2,eq3] - pendulum:de := generate [eq1,eq2,eq3] - setOutMode(14)$ck - setRedMode(1)$ck - complete pendulum changed: -de:=DE(jb,jbe); -ck:=CK(jb,jbe); de := JDE(jb, jbe); ck := CKP(jb, jbe); changed: -printSys [eq1,eq2,eq3,eq4,eq5] -pendulum:de := generate [eq1,eq2,eq3,eq4,eq5] printSys([eq1,eq2,eq3,eq4,eq5])$de pendulum:de := makeSystem [eq1,eq2,eq3,eq4,eq5] changed: -complete pendulum complete(pendulum)$ck
looking for completion of pendulum (constrained motion)
equations using multiindex notation (1 independent variable [t] and 3 dependent variables [x,y,F])
fricas
jb:=IJB('t,
Type: Type
fricas
jbe:=JBE jb;
Type: Type
fricas
de := JDE(jb,jbe);
Type: Type
fricas
ck := CKP(jb,jbe);
Type: Type
fricas
eq1:jbe := m*P(4,[1]) + U(1)/L*U(3)
 | (1) |
fricas
eq2:jbe := m*P(5,[1]) + U(2)/L*U(3) + m*g
 | (2) |
fricas
eq3:jbe := U(1)^2 + U(2)^2 - L^2
 | (3) |
fricas
eq4:jbe := P(1,[1]) - U(4)
 | (4) |
fricas
eq5:jbe := P(2,[1]) - U(5)
 | (5) |
fricas
printSys([eq1,eq2, eq3, eq4, eq5])$de
![\label{eq6}\begin{array}{c}
{\ }
\
{{{{L \ m \ {p_{1}^{4}}}+{{u^{1}}\ {u^{3}}}}\over L}= 0}
\
{\ }
\
{{{{L \ m \ {p_{1}^{5}}}+{{u^{2}}\ {u^{3}}}+{L \ g \ m}}\over L}= 0}
\
{\ }
\
{{{{u^{2}}^{2}}+{{u^{1}}^{2}}-{{L}^{2}}}= 0}
\
{\ }
\
{{-{u^{4}}+{p_{1}^{1}}}= 0}
\
{\ }
\
{{-{u^{5}}+{p_{1}^{2}}}= 0}
\](images/2399826850880044543-16.0px.png "\label{eq6}\begin{array}{c}
{\ }
\
{{{{L \ m \ {p_{1}^{4}}}+{{u^{1}}\ {u^{3}}}}\over L}= 0}
\
{\ }
\
{{{{L \ m \ {p_{1}^{5}}}+{{u^{2}}\ {u^{3}}}+{L \ g \ m}}\over L}= 0}
\
{\ }
\
{{{{u^{2}}^{2}}+{{u^{1}}^{2}}-{{L}^{2}}}= 0}
\
{\ }
\
{{-{u^{4}}+{p_{1}^{1}}}= 0}
\
{\ }
\
{{-{u^{5}}+{p_{1}^{2}}}= 0}
\") | (6) |
Type: OutputForm?
fricas
pendulum:de := makeSystem [eq1,eq2, eq3, eq4, eq5]
![\label{eq7}\begin{array}{c}
{\ }
\
{{{L \ m \ {p_{1}^{4}}}+{{u^{1}}\ {u^{3}}}}= 0}
\
{\ }
\
{{{L \ m \ {p_{1}^{5}}}+{{u^{2}}\ {u^{3}}}+{L \ g \ m}}= 0}
\
{\ }
\
{{-{u^{4}}+{p_{1}^{1}}}= 0}
\
{\ }
\
{{-{u^{5}}+{p_{1}^{2}}}= 0}
\
{\ }
\
{{{{u^{2}}^{2}}+{{u^{1}}^{2}}-{{L}^{2}}}= 0}
\](images/6844709053551123256-16.0px.png "\label{eq7}\begin{array}{c}
{\ }
\
{{{L \ m \ {p_{1}^{4}}}+{{u^{1}}\ {u^{3}}}}= 0}
\
{\ }
\
{{{L \ m \ {p_{1}^{5}}}+{{u^{2}}\ {u^{3}}}+{L \ g \ m}}= 0}
\
{\ }
\
{{-{u^{4}}+{p_{1}^{1}}}= 0}
\
{\ }
\
{{-{u^{5}}+{p_{1}^{2}}}= 0}
\
{\ }
\
{{{{u^{2}}^{2}}+{{u^{1}}^{2}}-{{L}^{2}}}= 0}
\") | (7) |
Type: JetDifferentialEquation?(IndexedJetBundle?(t,
fricas
setOutMode(14)$ck
 | (8) |
Type: NonNegativeInteger?
fricas
setRedMode(1)$ck
 | (9) |
Type: NonNegativeInteger?
fricas
complete(pendulum)$ck
![\label{eq10}\](images/7480555134030225570-16.0px.png "\label{eq10}\") | (10) |
 | (11) |
![\label{eq12}\](images/4218519603404177416-16.0px.png "\label{eq12}\") | (12) |
 | (13) |
 | (14) |
![\label{eq15}\begin{array}{c}
{\ }
\
{{{L \ m \ {p_{1}^{5}}}+{{u^{2}}\ {u^{3}}}+{L \ g \ m}}= 0}
\
{\ }
\
{{{L \ m \ {p_{1}^{4}}}+{{u^{1}}\ {u^{3}}}}= 0}
\
{\ }
\
{{-{u^{5}}+{p_{1}^{2}}}= 0}
\
{\ }
\
{{-{u^{4}}+{p_{1}^{1}}}= 0}
\
{\ }
\
{{{{u^{2}}^{2}}+{{u^{1}}^{2}}-{{L}^{2}}}= 0}
\](images/4679836929869205428-16.0px.png "\label{eq15}\begin{array}{c}
{\ }
\
{{{L \ m \ {p_{1}^{5}}}+{{u^{2}}\ {u^{3}}}+{L \ g \ m}}= 0}
\
{\ }
\
{{{L \ m \ {p_{1}^{4}}}+{{u^{1}}\ {u^{3}}}}= 0}
\
{\ }
\
{{-{u^{5}}+{p_{1}^{2}}}= 0}
\
{\ }
\
{{-{u^{4}}+{p_{1}^{1}}}= 0}
\
{\ }
\
{{{{u^{2}}^{2}}+{{u^{1}}^{2}}-{{L}^{2}}}= 0}
\") | (15) |
![\label{eq16}\](images/8817300687797269412-16.0px.png "\label{eq16}\") | (16) |
 | (17) |
Type: Void