Find angle giving highest rotated vector Z conponent (around X axis)

[JBlackhole]

To all

trying to remember my school days and the use of derivative (if that's the tool to use). Given the following

an X,Y,Z Cartesian co-ordinate system

a vector v with components (vx, vy, vz)

a rotation matrix around x-axis Rx(theta)

Header 1	Header 2	Header 3
1	0	0
0	cos(theta)	-sin(theta)
0	sin(theta)	cos(theta)

Is there a way of finding at which angle theta the z component is the highest?

Thanks

Regards

JXB

[AlanStevens]

The z component of the rotated vector will be  vy*sin(theta) + vz*cos(theta)

Differentiate wrt theta and set to zero to get the maximum theta as  thetamax = atan(vy/vz)

(Check that it is a maximum not a minimum!).

Alan

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[StuartBruff · Accepted solution]

J B wrote:

trying to remember my school days and the use of derivative (if that's the tool to use). Given the following

an X,Y,Z Cartesian co-ordinate system

a vector v with components (vx, vy, vz)

a rotation matrix around x-axis Rx(theta)

Header 1	Header 2	Header 3
1	0	0
0	cos(theta)	-sin(theta)
0	sin(theta)	cos(theta)

Is there a way of finding at which angle theta the z component is the highest?

Here's a starter for 10 ...

Stuart

[JBlackhole]

Thanks Stuart for the input.  A lot more that I anticipated! I can see what I need I think

[StuartBruff]

J B wrote:

Thanks Stuart for the input.  A lot more that I anticipated! I can see what I need I think

No worries, JXB.

Stuart