What effect does armature reaction have on the torque speed characteristic of a DC shunt motor?​

Compactly:
=+Higgs+lep.+qrk.+Yuk.
L
=
L
Y
M
+
L
H
i
g
g
s
+
L
l
e
p
.
+
L
q
r
k
.
+
L
Y
u
k
.

where
=−14Tr
L
Y
M
=
−
1
4
T
r
F
a
b
F
a
b

Higgs=−(†)()+14(†−122)2
L
H
i
g
g
s
=
−
(
D
a
ϕ
†
)
(
D
a
ϕ
)
+
1
4
λ
(
ϕ
†
ϕ
−
1
2
v
2
)
2

lep.=ℓ†⧸ℓ+¯†⧸¯
L
l
e
p
.
=
i
ℓ
I
†
⧸
D
ℓ
I
+
i
e
¯
I
†
⧸
D
e
¯
I

qrk.=†⧸+¯†⧸¯+¯†⧸¯
L
q
r
k
.
=
i
q
I
†
⧸
D
q
I
+
i
u
¯
I
†
⧸
D
u
¯
+
i
d
¯
I
†
⧸
D
d
¯
I

Yuk.=−ℓ¯−′¯
L
Y
u
k
.
=
−
y
I
J
ϕ
ℓ
I
e
¯
J
−
y
I
J
′
ϕ
q
I
d
¯
J

−″†¯+ℎ..
−
y
I
J
″
ϕ
†
q
I
u
¯
J
+
h
.
c
.

and specifying that F is the curvature on the gauge group ≃(3)⊗(2)⊗(1)
G
≃
S
U
(
3
)
⊗
S
U
(
2
)
⊗
U
(
1
)
,
D
a
is the gauge covariant derivative on G, ⧸
⧸
D
is the gauge covariant Dirac operator on G, and specifying the representations of the fields: the scalar
ϕ
in the rep (1,2,-1/2), and the fermions ℓ
ℓ
in the rep (1,2,-1/2), ¯
e
¯
in (1,1,+1),
q
in (3,2,+1/6), ¯
u
¯
in (3¯,1,−2/3)
(
3
¯
,
1
,
−
2
/
3
)
, and ¯
d
¯
in (3¯,1,+1/3)
(
3
¯
,
1
,
+
1
/
3
)
; where I is a generation index running over 1,2,3, and where everything else is a constant.
42.7K viewsView 50 upvotes · Answer requested by Mario Ng

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Joseph Heavner, mathematics student at the University of Maryland
Answered June 30, 2015 · Upvoted by Alon Amit, PhD in Mathematics; Mathcircler. and Sam Sinai, Ph.D student in Mathematical Biology

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