Derivatives / partial derivatives rule

[disb]

When I am taking a partial derivative of an equation with respect to theta_dot, then theta is constant, right?

What if I am taking partial derivative with respect to theta, will theta_dot be constant?

In this case, theta_dot = omega (angular velocity), but I must keep equation in terms of theta in order to find this equation of motion by Lagrangian methods.

Thanks in advanced to anyone that can help me!

 

[rock.freak667]

If you are finding ∂f/∂θ, then everything else other than θ is constant.


so if you had f=θ²+ω²+ωθ ⇒∂f/∂θ=2θ+ω

 

[disb]

So how would take partial derivative of:

y = .5*m*(L*theta_dot)^2 + .5*m*g*L*cos(theta)

1) partial y with respect to theta_dot

AND

2) partial y with respect to theta

 

[rock.freak667]

So how would take partial derivative of:

y = .5*m*(L*theta_dot)^2 + .5*m*g*L*cos(theta)

1) partial y with respect to theta_dotQUOTE]

Well m,g,L and θ would be constants. So the partial derivative of .5*m*g*L*cos(theta) w.r.t. θ(dot) is 0. So differentiate the first term now.

 

[disb]

Ok, and what about part 2 of my question?

"partial y w.r.t. theta" for the first term is..?

Is the first term a constant in this case??

 

[rock.freak667]

Ok, and what about part 2 of my question?

"partial y w.r.t. theta" for the first term is..?

Is the first term a constant in this case??

Yes. So differentiate the second term.

 

[disb]

nvm, i got it i think... i am just thinking too hard..

if its partial w.r.t theta(dot), then everything (like theta_double_dot or theta) is considered constant except theta(dot)

if partial w.r.t theta(triple dot), then everything is constant except theta(triple dot)

if partial w.r.t. u(double prime), then u(triple prime), u(prime) and everything else except u(double prime) is constant.

right?

 

[disb]

thanks rock,

took me a while to fully understand it and get it sunk in my head,,

i was just thinking to hard