SetAttributes[{l, m, g, k, l0}, Constant];
T = 1/2 m (Dt[r, t]^2 + r^2*Dt[\[CurlyPhi], t]^2);
V = 1/2 k (r - l0)^2 - m*g*r (1 - 1/2 \[CurlyPhi]^2);
T = T //. r -> (z + 1) l;
V = V //. {r -> (z + 1) l, l0 -> l - m*g/k};
T = Simplify[T]
V = Simplify[V]
比如说z和[CurlyPhi]及其导数都是无穷小量，如何省略掉多项式中高于三次的z和[CurlyPhi]的项及其乘积项

刚刚学mathematica，捣鼓了一天，借鉴了这个问题的回答https://tieba.baidu.com/p/5970083794
SetAttributes[{l, m, g, k, l0}, Constant];
T = 1/2 m (Dt[r, t]^2 + r^2*Dt[\[CurlyPhi], t]^2);
V = 1/2 k (r - l0)^2 - m*g*r (1 - 1/2 \[CurlyPhi]^2);
T = T //. r -> (z + 1) l
V = V //. {r -> (z + 1) l, l0 -> l - m*g/k}
Total[Cases[Expand[T],
m__ /; Total[
Exponent[m, #] & /@ {z, Dt[z, t], \[CurlyPhi],
Dt[\[CurlyPhi], t]}] < 4]]
Total[Cases[Expand[V],
m__ /; Total[
Exponent[m, #] & /@ {z, Dt[z, t], \[CurlyPhi],
Dt[\[CurlyPhi], t]}] < 4]]

series〔表达式，{z，0，3}〕