Geostationary orbits are essentially circular orbits with a period of essentially one sidereal day and an inclination of essentially zero.
What you term "wobbly geosynchronous orbits" have the first two qualifications but inclinations substantially different than zero.
The obvious choice for a geosynchronous orbit having a period of essentially one sidereal day that was neither a $e=0, \ i=0$ orbit nor a $e=0, \ i \ne 0$ orbit would be a $e \ne 0$ orbit, i.e. an elliptical orbit with a period of one sidereal day!
I went to https://celestrak.org/satcat/search.php and downloaded the CSV version then sorted it with the scrappy script at the end. I kept data where the periods were between 1434.0 and 1437.5 minutes because there was a pronounced peak there.
Geosynchronous satellites are always jiggling around due to imperfect station keeping or being caught in the middle of a slow, electric propulsion induced station-keeping or longitude-changing maneuver.
Note also that when folks want to "park" two or three (or more?) satellites in the same longitude slot, they use slight offsets in both eccentricity and inclination to create a "special kind of wobble" that is very small, but reliably keeps them from hitting each other for a while. How does the "eccentricity-inclination vector separation" technique work for colocated GEO satellites?
But I found about 10 geosynchronous satellites with moderate eccentricities between about 0.06 and 0.14, and a few very high-fliers with larger eccentricities.
So:
Are there any satellites in geosynchronous orbits that are neither geostationary nor 'wobbly geostastionary' (figure of eight geostationary)?
Yes!
Wobbly and not-wobbly geosynchronous orbits that the OP has described:
From here.
Python script for plot, uses CSV SATCAT data downloaded from Celestrak as described above.
import numpy as np
import matplotlib.pyplot as plt
fname = 'satcat oo102.csv'
with open(fname, 'r') as infile:
lines = infile.readlines()
datal = []
for line in lines[1:]:
try:
datal.append([float(x) for x in line.split(',')[9:13]])
except:
pass
data = np.array(list(zip(*datal)))
period = data[0]
fig, (ax1, ax2, ax3) = plt.subplots(3, 1)
a, b = np.histogram(period, bins=np.arange(1400, 1500, 0.2))
ax1.plot(b[1:], a, '-k')
keep = (period >= 1434) * (period <= 1437.5)
period = data[0]
period, inclination, apo, peri = data[:, keep]
a, b = np.histogram(period, bins=np.arange(1400, 1500, 0.2))
ax1.plot(b[1:], a, '-r')
ax1.set_yscale('log')
eccentricity = (apo - peri) / (apo + peri + 2 * 6378.137)
for ax in (ax2, ax3):
ax.plot(inclination, eccentricity, '.k')
ax.set_xlabel('inclination (deg)')
ax.set_ylabel('eccentricity')
ax2.set_ylim(0, 0.15)
plt.show()
"""
0 OBJECT_NAME
1 OBJECT_ID
2 NORAD_CAT_ID
3 OBJECT_TYPE
4 OPS_STATUS_CODE
5 OWNER
6 LAUNCH_DATE
7 LAUNCH_SITE
8 DECAY_DATE
9 PERIOD
10 INCLINATION
11 APOGEE
12 PERIGEE
13 RCS
14 DATA_STATUS_CODE
15 ORBIT_CENTER
16 ORBIT_TYPE
"""
