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

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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

Calculus_Derivatives

S

StuartBruffAnswer

23-Emerald V

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

A

AlanStevens

19-Tanzanite

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

Answer

23-Emerald V

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?