Derivados superiores del vector de posición con respecto al tiempo
Tiempo-derivativos de posición En física, las cuarta, quinta y sexta derivadas de la posición se definen como derivadas del vector de posición con respecto al tiempo; las derivadas primera, segunda y tercera son la velocidad, la aceleración y idiota, respectivamente. Las derivadas de orden superior son menos comunes que las tres primeras; por lo tanto, sus nombres no están tan estandarizados, aunque el concepto de trayectoria rápida mínima se ha utilizado en robótica y se implementa en MATLAB.
La cuarta derivada a menudo se denomina chasquido o rebote . El nombre "snap" para la cuarta derivada condujo a crackle y pop para la quinta y sexta derivadas respectivamente, inspiradas en las mascotas de Rice Krispies, Snap, Crackle y Pop. Estos términos se utilizan ocasionalmente, aunque "a veces de manera algo jocosa".
Cuarta derivada (chasquido/rebote) El chasquido, o rebote, es la cuarta derivada del vector de posición con respecto al tiempo, o la tasa de cambio del tirón con respecto al tiempo. De manera equivalente, es la segunda derivada de la aceleración o la tercera derivada de la velocidad,
y está definido por cualquiera de las siguientes expresiones equivalentes:
s → → = d ȷ ȷ → → d t = d 2 a → → d t 2 = d 3 v → → d t 3 = d 4 r → → d t 4 . {\displaystyle {\vec}={\frac} {\fnMicrosoft Sans Serif} } {dt}={\frac {}{2}{\vec} {} {\fn}} {\fnMicroc}}} {\fnMicroc}}} {\f}}} {\f}}}} {\fn}} {\f}}}} {\fn}}} {\f}}} {\f}}} {\f} {\f}}}}} {\f}}}}}}} {\f}} {\f}}}}}}} {\f}}}}}} {\f}}}} {\f}}}}} {\f}}}} {\f}} {\f}} {\f}}}}} {\f}}}}}}}} {\f}}}}}} {\f} {\f} {\f}}}}}}} {\f}} {\f}}}}}}}}}} {\f} {\f}}} {\f}}}}}}}}}}}}}}}} {\f}}}}}}}}} {\fnK} {\fnMicrosoft} {\fnK} {\f}} {\fnMicroc}}}} {\f}} {\f}}} {\f}}} {\f}}} {\f}}}} {\f}}} {\f}}}} {\f}} {\f}} {\f}}}}}} {\f}}}}} {\f}}}}}} {\f} {\f}}}}}}}}} {\f}}}}}}}} {\f}}} {\f}}} {\f}} {\f}} {\f}}} {\f}}}}}}}}} {\f}}}}}} {\f} {\f} {\f}} {\f}} {\f}}}}} {\f} {\f}} {\f} {\f}}}}}}}} {\f}}}}}}}}}}}}}}}}}}}}}}}}}} {\fnK} {\fnMicrosoft Sans Serif} {\fnMicrosoft} {\fnMicrosoft} {\fn} {\fnK}}} {\fnK}} {\fnK}} {\fnK}} {\f}} {\fn\f}}}} {\fn\fn\fn\fn\f}}\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\f}\fn\fn\fn\fn\fn\fn\f}\fn\fn\fn\fn\fn\fn\fn\f}}\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\f}}}}}}\fn {}} {dt^{4}}}}
Las siguientes ecuaciones se utilizan para un ajuste constante:
ȷ ȷ → → = ȷ ȷ → → 0 + s → → t , a → → = a → → 0 + ȷ ȷ → → 0 t + 1 2 s → → t 2 , v → → = v → → 0 + a → → 0 t + 1 2 ȷ ȷ → → 0 t 2 + 1 6 s → → t 3 , r → → = r → → 0 + v → → 0 t + 1 2 a → → 0 t 2 + 1 6 ȷ ȷ → → 0 t 3 + 1 24 s → → t 4 , {\displaystyle {\begin{aligned}{\vec} {\jmat } âTMa {\jmath }_{0}+{\vec {s} t,\\\{\vec} {a} {\fn} {\fnMic} {a}_{0}+{\vec} {\fnMit - No. {2}{2} {\fnK} {\\fnK}} {\\fnK} {\f} {\f} {\fn} {\fnK}}} {\fnK} {\fnK}} {\fnK} {\f} {\fnK} {\f}}\fnK\f}\f}\fnK\f} {\f}}\f}\f}}\f}\f}\f}\f}\f}\f}\f}\f}\\f}\f}\f}\f}\\\f}\fnK\fn\fn\f}\f}\f}\f}\\fnK\fnK\fnK\fnK\fnK\\\\\\\\\fnK\fnK\fnK\\fnK\fnK\fnK\fnK\f}\fnK\fnK\fnK\f}\\\fn {\fnK} {\fnh}\fnh}\fn\fnh} {a}_{0}t+{\tfrac} {1}{2}{\vec\jmath }_{0}t^{2}+{\tfrac {1}{6} {\fn} {\fnK} {\fn}} {\\fn} {\fn} {\\fn}} {\fn} {\fn}}} {\fn}}} {\\fn\fn}} {\\\fn\f}}}} {\\\\fn\fn\fnK\f}}}}}}}\\\\\\\\\\\\\\\\\\\\\\\\\\\fn\\\fn\fn\\fnK\fn\fnK\fnK\fn\fn\fn\fn\fn\fn\fn\fnK\fn\fn\fn\fn}}\\\\\\fn\fn\fn\fn\fn\fn\fn}\fn\fn\fn\\fn\fn\\fn\fn\fn\\\\fn {\fnh} {\fnh}\fnh}\fn\fnh} {\fnMicroc} {\fnMicroc} {1}{2}{\vec} {\fnh} {\fn} {\fnK}} {\fn\fn\fn\fnh}} {\fn}\fn\fn}\fn}\fn\fn\fn\fn\fn\fn} {1}{6}{\vec\jmath }_{0}t^{3}+{\tfrac {1}{24} {\fnK} {4} {\fnK} {\fnK}} {\fnK}} {\fn}} {\fn9}} {\fn9}} {\fn9}}} {\fn9}}}} {\fn9}} {\fn9}}} {\f}}} {\f}}}} {\f}}}}}}}}}}}} {\f}}}}}}}}}}}} {\f}} {\f}}}} {\f} {\f}} {\f}}}}}}}}}}}}}}}}}}}}}}}}}}}} {\f} {\f} {\f}}} {\f}}} {\f} {\f} {\f}}} {\f}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
dónde
s → → {\displaystyle {\vec}} ȷ ȷ → → 0 {\fnMicrosoft {\fnMith} }_{0} ȷ ȷ → → {\displaystyle {\vec {\jmath}}} a → → 0 {\displaystyle {\vec {a}_{0} a → → {\displaystyle {\vec}} v → → 0 {\displaystyle {\vec}_{0}} v → → {\displaystyle {\vec}} r → → 0 {\displaystyle {\vec}_{0}} r → → {\displaystyle {\vec}} t {\displaystyle t} La notación s → → {\displaystyle {\vec}}
Las dimensiones del ajuste son la distancia por cuarta potencia del tiempo (LT−4 ). La unidad SI correspondiente es metro por segundo a la cuarta potencia, m/s4 , m⋅s−4 .
Quinta derivada (feminine)
La quinta derivada del vector de posición con respecto al tiempo a veces se denomina crujido. Es la tasa de cambio del snap con respecto al tiempo. Crackle se define mediante cualquiera de las siguientes expresiones equivalentes:
c → → = d s → → d t = d 2 ȷ ȷ → → d t 2 = d 3 a → → d t 3 = d 4 v → → d t 4 = d 5 r → → d t 5 {\displaystyle {\vec}={\frac} {\fnMic} {} {\fn}} {\fnMicroc}}} {\fnMicroc}}} {\f}}}} {\f}}} {\fn}}} {\f}}}} {\fn}}} {\fn}} {\f}}}} {\f}}}}}} {\f}}}} {\f}} {\f}}}}} {\f}}}}}} {\f}}}}}}} {\f}}}}}} {\f}}}}} {\f}}} {\f} {\f}}} {\f}}}}}}}}} {\f}}}}}}} {\f}} {\f} {\f}}}}}} {\f}}} {\f}}}}}}}} {\f} {\f} {\f}}}}}}}}} {\f}}}}}}}}}}}}}}}}}}}} {}{2}{\vec} {\fnMit {\fnK}} {\fnMicroc} {\fnK} {\fnMicrosoft} {} {\fn}} {\fnMicroc}}} {\fnMicroc}}} {\fn}} {\fn}}}}} {\fn}} {\fn}}} {\fn}}} {\fn}}} {\f}}} {\f}}}}} {\f}}}}}} {\f}}}} {\f}}}}}}} {\f}}}}}} {\f}}}}} {\f}}}}} {\f}}}} {\f} {\f}}}}}}}} {\f}}}}} {\f}}}}}}}}}} {\f} {\f} {\f} {\f}}} {\f}}} {\f} {\f}}}}}}} {\f}} {\f}}}}}}}}}}}}}}}}}}}}} {\f}}}}}}}} {\fnK} {\fnMicrosoft Sans Serif} {\fnMicrosoft} {\fnMicrosoft} {\fn} {\fnK}}} {\fnK}} {\fnK}} {\fnK}} {\f}} {\fn\f}}}} {\fn\fn\fn\fn\f}}\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\f}\fn\fn\fn\fn\fn\fn\f}\fn\fn\fn\fn\fn\fn\fn\f}}\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\f}}}}}}\fn {} {\fn}} {\fnMicroc}}} {\fnMicroc}}} {\f}}} {\f}}}} {\fn}}}} {\f}}} {\fn}} {\f}}}} {\f}}}} {\f}}}}}} {\f}}}}}} {\f}}} {\f}}}}}}} {\f}}} {\f}}}} {\f}}}}} {\f}}}} {\f}}} {\f} {\f}}}}}} {\f}}}}}}}} {\f}}}}}}} {\f} {\f} {\f} {\f}}} {\f}}} {\f}}}}}}}}}}} {\f} {\f} {\f}}}}}}}}}}}} {\f}}}}}}}}}}}}}}} {\fnK} {\fnMic} {}} {dt} {5}}} {}} {}}} {}}} {}}} {}}} {}}}}} {}}}}}}} {}}}}}} {}}}} {}}}}}}} {}}}} {}}}}}} {}}}}}}}}}} {}}}}}}}} {}} {}}}}}}}}} {}}}}}}} {}}}}}}}}} {} {}}}}}}}}}} {}}}}}} {} {}}}} {}}}}} {}}}}}}} {}}}}}}}} {} {} {}}}}} {}}}}}}}}}}}}} {}}}}}}}}}}}} {}}}}}}} {}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
Las siguientes ecuaciones se utilizan para un crujido constante:
s → → = s → → 0 + c → → t ȷ ȷ → → = ȷ ȷ → → 0 + s → → 0 t + 1 2 c → → t 2 a → → = a → → 0 + ȷ ȷ → → 0 t + 1 2 s → → 0 t 2 + 1 6 c → → t 3 v → → = v → → 0 + a → → 0 t + 1 2 ȷ ȷ → → 0 t 2 + 1 6 s → → 0 t 3 + 1 24 c → → t 4 r → → = r → → 0 + v → → 0 t + 1 2 a → → 0 t 2 + 1 6 ȷ ȷ → → 0 t 3 + 1 24 s → → 0 t 4 + 1 120 c → → t 5 {\displaystyle {\begin{aligned}{\vec} {\fnMicrosoft} {\fnMicrosoft} {\fnMicrosoft Sans Serif} {\fnMicrosoft Sans Serif} {\fnMicrosoft Sans Serif}} {\fnMicrosoft}} {\fnMicrosoft Sans Serif} {\fnMicrosoft Sans} {\fnMicrosoft}} {\fnMicrox}}}}\\\fnMicrox}}}}}}\\\\\\\\\fnMicros}}\\\\\\\\\\\\\\\\fnMinMinMinMinMinMinMinMinMinMinMinMinMinK}}}}}}}}}}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\s}}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ }_{0}+{\vec {\fnMicroc} {1}{2}{\vec}\,t^{2}\[1ex]{\vec} {a} {\fn} {\fnMic} {a}_{0}+{\vec} {\fnMit }_{0}\,t+{\tfrac {1}{2}{\vec} {\fnMicroc} {1}{6}{\f}\,t^{3}\[1ex]{\vec {\f} {\fn} {\fn} {\fnK} {\fn0} {\fn0} {\fn0}} {\fn0} {\fn0}}}\\\fnK\fn0}\fn0}\\fnK\fnK\fn0}\fnK\fnK\fnK\fn9}\fnK\fnK\fnK\fnK\fnK\fnK\fnK\fnK\fnK\f}\fnK\f}\fnK\fnK\fnK\fnK\f}}\fnK}\fnK\f}\fnK\fnK\fnK\fnK\fnK\fnK\fnK\f}\fnK\fnK\fnK}}}}}}\fn {\fnK} {\fnh}\fnh}\fn\fnh} {a}_{0}\,t+{\tfrac} {1}{2}{\vec\jmath }_{0}\,t^{2}+{\tfrac {1}{6}{\vec} {\fnMicroc} {1}{24}{\f}\,t^{4}\[1ex]{\vec {r} {\vec} {\vec}={\vec} {\fnh} {\fnh}\fnh}\fn\fnh} {\fnMicroc} {1}{2}{\vec} {\fnMicroc} {1}{6}{\vec\jmath }_{0}\,t^{3}+{\tfrac {1}{24}{\vec} {\fnMicroc} {1}{120}{\vec}\,t^{5}\end{aligned}
dónde
c → → {\displaystyle {\vec}} s → → 0 {\displaystyle {\vec {\fnMicrosoft} s → → {\displaystyle {\vec}} ȷ ȷ → → 0 {\fnMicrosoft {\fnMith} }_{0} ȷ ȷ → → {\displaystyle {\vec {\jmath}}} a → → 0 {\displaystyle {\vec {a}_{0} a → → {\displaystyle {\vec}} v → → 0 {\displaystyle {\vec}_{0}} v → → {\displaystyle {\vec}} r → → 0 {\displaystyle {\vec}_{0}} r → → {\displaystyle {\vec}} t {\displaystyle t} Las dimensiones del crujido son LT−5 . La unidad SI correspondiente es m/s5 .
Sexta derivada (feminine)
La sexta derivada del vector de posición con respecto al tiempo a veces se denomina pop. Es la tasa de cambio del crepitante con respecto al tiempo. Pop se define mediante cualquiera de las siguientes expresiones equivalentes:
p → → = d c → → d t = d 2 s → → d t 2 = d 3 ȷ ȷ → → d t 3 = d 4 a → → d t 4 = d 5 v → → d t 5 = d 6 r → → d t 6 {\displaystyle {\vec}={\frac} {\fnMic} {c} {dt}={\frac} {}{2}{\vec} {\fnMicroc} {\fnMicroc}}} {\fnMicroc}}} {\f}}} {\f}}} {\f}}}} {\f}}} {\fn}}}} {\f}}}}} {\f}}}}} {\f}}}}} {\f}}}} {\f}}}}} {\f}}}}}}} {\f}}}}}} {\f}}}}} {\f}}}}}} {\f}}}} {\f} {\f}}}}}}} {\f}}}} {\f}}}}}}}}}}} {\f} {\f} {\f} {\f}} {\f}}}}}}}} {\f}}}}}}}}}}}}}} {\f}}}}}}}}}}}}}}}}}}}} {\f}}}}}}} {\fnK} {\fnMicrosoft} {\fnK} {\fnMicroc}} {\fnMicroc}} {\fnK}}} {\fnK}}}} {\fn}}} {\fn}}}} {\fn}}} {\fn}}}} {\fn\f}}}}}} {\fn\f}}}}}} {\f}}}}}}}}}}} {\f}}}}}} {\f}}}}}} {\f}}}}} {\f}}}} {\f}}} {\f}}}}}}}}}}}}}}}}}}}} {\f}}}} {\f} {\f} {\f} {\f}}}}}}}}}} {\f}}}}}\f}}} {\f}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} {\f}}}} {\fnK} {\fnMicrosoft Sans Serif} {\fnMicrosoft} {\fnMicrosoft} {\fn} {\fnK}}} {\fnK}} {\fnK}} {\fnK}} {\f}} {\fn\f}}}} {\fn\fn\fn\fn\f}}\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\f}\fn\fn\fn\fn\fn\fn\f}\fn\fn\fn\fn\fn\fn\fn\f}}\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\fn\f}}}}}}\fn {} {\fn}} {\fnK}} {\fnMicroc}}} {\f}}} {\f}} {\f}}}} {\fn}}} {\f}}} {\fn}}} {\fn}}}} {\f}} {\f}}}}} {\f}}}}} {\f}}}}} {\f}}}}}}} {\f}}}}}}} {\f}}}}} {\f}}}}} {\f}}}} {\f} {\f}}}}}}} {\f}}}} {\f}}}}}}}}}} {\f} {\f} {\f} {\f}}} {\f}}}}}} {\f} {\f} {\f}} {\f}}}}}}} {\f}}}}}}}}}} {\f}}}}}}}}}}}}} {\fnK} {\fnMic} {} {\fn}} {\fnK}}} {\fnMic}}} {\fnK}}}} {\f}}}} {\fn}} {\f}}}} {\fn}}}} {\fn}}} {\f}}} {\f}}}}} {\f}}}}}} {\f}}}} {\f}}}}}}}} {\f}}} {\f}}}} {\f}}}}}}} {\f}}}}} {\f} {\f} {\f}}}} {\f}}}}}}}}} {\f}}}}} {\f} {\f} {\f}} {\f}} {\f}}}}}}}}} {\f} {\f}}} {\f}}}}}}}}}}}}}}}}}}}}}} {\f}}}}}}}}}}}} {\fnK} {\fnMic} {}} {dt} {6}}} {}} {}}} {}}} {}}} {}}} {}}}} {}}}}}}} {}}}}}}} {}}}} {}}}}}} {}}}}} {}}}}}} {}}}}} {}}}}}}} {}}}}}}} {}}}}}}}} {}}}}}}} {}}}}}}}}}} {}} {}} {}}}}}}} {}}}}}}} {}}} {}}}}}}}}}}}}}} {} {}}}}} {}} {} {} {}}}} {}}}}}}}}}}}}} {}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}} {
Las siguientes ecuaciones se utilizan para pop constante:
c → → = c → → 0 + p → → t s → → = s → → 0 + c → → 0 t + 1 2 p → → t 2 ȷ ȷ → → = ȷ ȷ → → 0 + s → → 0 t + 1 2 c → → 0 t 2 + 1 6 p → → t 3 a → → = a → → 0 + ȷ ȷ → → 0 t + 1 2 s → → 0 t 2 + 1 6 c → → 0 t 3 + 1 24 p → → t 4 v → → = v → → 0 + a → → 0 t + 1 2 ȷ ȷ → → 0 t 2 + 1 6 s → → 0 t 3 + 1 24 c → → 0 t 4 + 1 120 p → → t 5 r → → = r → → 0 + v → → 0 t + 1 2 a → → 0 t 2 + 1 6 ȷ ȷ → → 0 t 3 + 1 24 s → → 0 t 4 + 1 120 c → → 0 t 5 + 1 720 p → → t 6 {\displaystyle {\begin{aligned}{\vec} {c}} {\vec} {c}_{0}+{\vec} {p}\,t\\\\\fnMic} {\fnMicrosoft} {\fnMicrosoft} {\fnMicrosoft Sans} {c}_{0}\,t+{\tfrac} {1}{2}{\vec} {p}\,t^{2}\\\\fnMic} {\jmat } âTMa {\jmath }_{0}+{\vec {\fnMicroc} {1}{2}{\vec} {c}_{0}\,t^{2}+{\tfrac} {1}{6}{\vec} {p}\,t^{3}\{\fnMic} {a} {\fn} {\fnMic} {a}_{0}+{\vec} {\fnMit }_{0}\,t+{\tfrac {1}{2}{\vec} {\fnMicroc} {1}{6}{\vec} {c}_{0}\,t^{3}+{\tfrac} {1}{24}{\vec} {p}\,t^{4}\\{\fnMic} {\fnK} {\fnK} {\fnh}\fnh}\fn\fnh} {a}_{0}\,t+{\tfrac} {1}{2}{\vec\jmath }_{0}\,t^{2}+{\tfrac {1}{6}{\vec} {\fnMicroc} {1}{24}{\vec} {c}_{0}\,t^{4}+{\tfrac} {1}{120}{\vec} {p}\,t^{5}\ {\fnMic} {\fnMicrosoft} {\fnK} {\fnh} {\fnh}\fnh}\fn\fnh} {\fnMicroc} {1}{2}{\vec} {\fnMicroc} {1}{6}{\vec\jmath }_{0}\,t^{3}+{\tfrac {1}{24}{\vec} {\fnMicroc} {1}{120}{\vec} {c}_{0}\,t^{5}+{\tfrac} {1} {720} {\fnK}} {\fnMicrosoft}} {\fn}} {\fn}} {\fn}} {\fn}}}} {\fn}} {\fn}}} {\fn}}}} {\f}}} {\f}}}}}}} {\f}}}}}}}}}} {\f}}}}}}}}}}}}}}} {\f}} {\f}}}}}}}}} {\f}}}}} {\f}}}}}}}}}}}} {\f}}}}}}}}} {\f}}}}}}}}}} {\f}} {\f}}}}}}}}}}}}} {\f}} {\f}}}}} {\f}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
dónde
p → → {\displaystyle {\vec}} c → → 0 {\displaystyle {\vec {c}_{0} c → → {\displaystyle {\vec}} s → → 0 {\displaystyle {\vec {\fnMicrosoft} s → → {\displaystyle {\vec}} ȷ ȷ → → 0 {\fnMicrosoft {\fnMith} }_{0} ȷ ȷ → → {\displaystyle {\vec {\jmath}}} a → → 0 {\displaystyle {\vec {a}_{0} a → → {\displaystyle {\vec}} v → → 0 {\displaystyle {\vec}_{0}} v → → {\displaystyle {\vec}} r → → 0 {\displaystyle {\vec}_{0}} r → → {\displaystyle {\vec}} t {\displaystyle t} Las dimensiones del pop son LT−6 . La unidad SI correspondiente es m/s6 .
Más resultados...
![{\displaystyle {\begin{aligned}{\vec {s}}&={\vec {s}}_{0}+{\vec {c}}\,t\\[1ex]{\vec {\jmath }}&={\vec {\jmath }}_{0}+{\vec {s}}_{0}\,t+{\tfrac {1}{2}}{\vec {c}}\,t^{2}\\[1ex]{\vec {a}}&={\vec {a}}_{0}+{\vec {\jmath }}_{0}\,t+{\tfrac {1}{2}}{\vec {s}}_{0}\,t^{2}+{\tfrac {1}{6}}{\vec {c}}\,t^{3}\\[1ex]{\vec {v}}&={\vec {v}}_{0}+{\vec {a}}_{0}\,t+{\tfrac {1}{2}}{\vec {\jmath }}_{0}\,t^{2}+{\tfrac {1}{6}}{\vec {s}}_{0}\,t^{3}+{\tfrac {1}{24}}{\vec {c}}\,t^{4}\\[1ex]{\vec {r}}&={\vec {r}}_{0}+{\vec {v}}_{0}\,t+{\tfrac {1}{2}}{\vec {a}}_{0}\,t^{2}+{\tfrac {1}{6}}{\vec {\jmath }}_{0}\,t^{3}+{\tfrac {1}{24}}{\vec {s}}_{0}\,t^{4}+{\tfrac {1}{120}}{\vec {c}}\,t^{5}\end{aligned}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13172ed785d84cc18fbe636c060d7813f67a69d6)
