Free Vibrations of a linear triatomic molecule

In summary, the conversation is about equation 6.59 in Classical Mechanics Goldstein 3rd edition and how to reach a certain step in the process. The speaker is struggling to understand how to reach this step and mentions taking the inverse of equation 6.41. They also mention trying to upload a screenshot of the textbook for reference. Another person offers guidance and asks for the original matrix A. The conversation ends with the speaker providing the original matrix and mentioning inverting it.
  • #1
Ben Geoffrey
16
0
This question is regarding equation 6.59 in Classical Mechanics Goldstein 3rd edition. I don't understand how he reaches that step. He says he does by inverting 6.41. Is he taking the transpose matrix composed of the eigen vectors by meaning inversion ?

I thought I could upload the screenshot of the page of the book but the option is not provided. So please look up the textbook if you could to help me out. Thank you. Sorry for the inconvenience
 
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  • #2
Ben Geoffrey said:
I thought I could upload the screenshot of the page of the book but the option is not provided.

of course you can upload a screenshot, use the upload button and upload the image file ... gif or jpg preferredDave
 
  • #3
Ben Geoffrey said:
I thought I could upload the screenshot of the page of the book but the option is not provided. So please look up the textbook if you could to help me out. Thank you. Sorry for the inconvenience
You may not be able to upload if you are using the mobile PF App. Try a laptop or tablet running a Browser -- that should work for you. :smile:
 
  • #4
Ok I will help you with these pictures, but can you show your work? :wink:
 

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Likes berkeman
  • #5
Okay Thanks for the guidance. So The results he gets are in the picture names 'Physics forums' and he says he gets them by inverting this equation show in the picture 'Physics forum 1'. I inverted the aij matrix to aji since it is an orthogonal matrix. But I am not getting the same answers. Can anyone help ?
 

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  • #6
What do you get for the original matrix A?
 
  • #7
This is the original matrix. So I just transpose it and the rows become columns and columns become rows.
 

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Related to Free Vibrations of a linear triatomic molecule

1. What is a linear triatomic molecule?

A linear triatomic molecule is a molecule composed of three atoms that are arranged in a straight line. This type of molecule is commonly found in diatomic molecules, such as carbon dioxide (CO2) and nitrogen dioxide (NO2).

2. What are free vibrations of a linear triatomic molecule?

Free vibrations of a linear triatomic molecule refer to the natural oscillations or vibrations that the molecule undergoes without any external forces acting on it. This can be imagined as the molecule "wiggling" back and forth along its bond axis.

3. How are the vibrational modes of a linear triatomic molecule classified?

The vibrational modes of a linear triatomic molecule are classified as symmetric and asymmetric stretches, as well as bends. Symmetric stretches involve the atoms moving in the same direction, while asymmetric stretches involve the atoms moving in opposite directions. Bends refer to the atoms moving in a perpendicular direction to the bond axis.

4. Why is the study of free vibrations of a linear triatomic molecule important?

Studying the free vibrations of a linear triatomic molecule is important for understanding the fundamental principles of molecular vibrations and their role in chemical reactions. This knowledge is crucial for fields such as materials science, atmospheric chemistry, and biochemistry.

5. How can the free vibrations of a linear triatomic molecule be experimentally observed?

The free vibrations of a linear triatomic molecule can be observed using various spectroscopic techniques, such as infrared spectroscopy or Raman spectroscopy. These techniques measure the absorption or scattering of light by the molecule, providing information about its vibrational modes.

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