Calc Euler Rotation Vector: Eurasia-North America | Lat/Long Pole

[hrr379]

Calculate the Euler rotation vector for Eurasia relative to North
America. The rotation vectors for Eurasia and North America relative
to the Pacific are _pacω_eur = [0.000529,-0.007235, 0.013123] and
_pacω_NA = [0.001768 -0.008439 0.009817]. Also, give the latitude and longitude of the pole of relative rotation

I was hoping if someone is kind enough to show me how to calculate latitude and longitude of the pole of relative rotation. Thanking for whoever helps a damsel in distress.

 

[Aaron Bex]

The Euler rotation vector for Eurasia relative to North America can be calculated using the following equation:

eurωNA = pacωeur - pacωNA

eurωNA = [0.000529, -0.007235, 0.013123] - [0.001768 -0.008439 0.009817]

eurωNA = [-0.001239, 0.000704, 0.003306]

The latitude and longitude of the pole of relative rotation can be calculated using the following equation:

lat = arcsin(eurωNAz), lon = arctan2(eurωNAy, eurωNAx)

lat = arcsin(0.003306) = 1.81°
lon = arctan2(0.000704, -0.001239) = -90.01°

Therefore, the latitude and longitude of the pole of relative rotation is (1.81°, -90.01°).

 

[Huyen401]

Sure, I'd be happy to help! To calculate the Euler rotation vector for Eurasia relative to North America, we can use the formula ωeur = ωNA - ωpac, where ωeur is the rotation vector for Eurasia, ωNA is the rotation vector for North America, and ωpac is the rotation vector for the Pacific.

Substituting the given values, we get: ωeur = [0.001768 -0.008439 0.009817] - [0.000529,-0.007235, 0.013123] = [0.001239 -0.001204 -0.003306]

To calculate the latitude and longitude of the pole of relative rotation, we can use the following formula:

λ = atan2(ωy, ωx)
φ = asin(ωz)

where λ is the longitude, φ is the latitude, ωx and ωy are the first two components of the rotation vector, and ωz is the third component.

Substituting the values from our calculated rotation vector, we get:

λ = atan2(-0.001204, 0.001239) = -45.975 degrees
φ = asin(-0.003306) = -0.189 degrees

Therefore, the latitude of the pole of relative rotation is approximately -0.189 degrees and the longitude is approximately -45.975 degrees.

I hope this helps! Don't hesitate to ask if you have any further questions.