Computatuion of v_i (t+ 0.5 *delta t) and omega_i (t+ 0.5 *delta t).

[Srishti-Siddharth-iitb]

I am trying to simulate a single Cosserat rod in MATLAB using your codes and the numerical scheme discussed in the following 2018 paper: https://doi.org/10.1098/rsos.171628. According to equations (C5) and (C6) of the paper (page 25), the position and orientation at (t+delta t) can be computed using v_i (t+ 0.5 delta t) and omega_i (t+ 0.5 delta t). Could you please confirm whether these velocities have been computed using the following formulae in your Python code?

v_i (t+ 0.5 delta t) = v_i (t) +0.5 delta t dv_dt(t+0.5 delta t),

and

omega_i (t+ 0.5 delta t) = omega_i (t) +0.5 delta t domega_dt(t+0.5 delta t),

[armantekinalp]

There is a typo there. You can use the above equations.

[Srishti-Siddharth-iitb]

Thank you.

On Thu, Jul 25, 2024 at 2:46 AM Arman Tekinalp @.***> wrote:

Screen.Shot.2024-07-24.at.4.15.09.PM.png (view on web) https://github.com/user-attachments/assets/6d51de7c-61e2-4c0a-b7d1-f112345f58b8

There is a typo there. You can use the above equations.

— Reply to this email directly, view it on GitHub https://github.com/GazzolaLab/PyElastica/issues/420#issuecomment-2248912438, or unsubscribe https://github.com/notifications/unsubscribe-auth/AXRBXIM4EXRH5V5BJAOWSO3ZOAKRVAVCNFSM6AAAAABLNGA43CVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDENBYHEYTENBTHA . You are receiving this because you authored the thread.Message ID: @.***>

[Srishti-Siddharth-iitb]

Hello, I hope I am not bothering you with the questions about the PyElastica code. I had a doubt regarding the modified equations which you have sent as a screenshot in this email thread. Specifically, to compute $\Dot{v} (t+0.5 \delta t)$ and $\Dot{w} (t+0.5 \delta t)$, one would need the values of $v ( t+0.5 \delta t )$ and $w ( t+0.5 \delta t )$ to compute the discrete versions of Lagrangian transport and unsteady dilation given in Equation (3.9) in https://doi.org/10.1098/rsos.171628. I was wondering whether $v ( t+0.5 \delta t )$ and $w ( t+0.5 \delta t )$ should've computed as follows:

1. $v ( t+0.5 \delta t ) = v(t) + 0.5 \delta t \Dot{v} (t) , and
2. $w ( t+0.5 \delta t ) = w(t) + 0.5 \delta t \Dot{w} (t).

Thank you again for all the help.

Regards Srishti

On Fri, Jul 26, 2024 at 1:48 PM Srishti siddharth < @.***> wrote:

Thank you.

On Thu, Jul 25, 2024 at 2:46 AM Arman Tekinalp @.***> wrote:

Screen.Shot.2024-07-24.at.4.15.09.PM.png (view on web) https://github.com/user-attachments/assets/6d51de7c-61e2-4c0a-b7d1-f112345f58b8

There is a typo there. You can use the above equations.

— Reply to this email directly, view it on GitHub https://github.com/GazzolaLab/PyElastica/issues/420#issuecomment-2248912438, or unsubscribe https://github.com/notifications/unsubscribe-auth/AXRBXIM4EXRH5V5BJAOWSO3ZOAKRVAVCNFSM6AAAAABLNGA43CVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDENBYHEYTENBTHA . You are receiving this because you authored the thread.Message ID: @.***>

[sy-cui]

In our code we use $\omega$ at time $t$, although I do think you can use the formulae you proposed. For the time-stepping method we use (Verlet integration) to be applicable, technically $d\omega/dt$ should not be a function of $\omega$. However, the unsteady dilatation and Lagrangian transport terms are rarely important, and the overall algorithm is first-order accurate in time nonetheless.

[armantekinalp]

I am converting this to a discussion since it more about the methods, than code issue.