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

[QUOTE=disb;2697291]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

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