Exploring Holonomic Basis in Cartesian Coordinates

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SUMMARY

The discussion centers on the properties of Cartesian coordinates, specifically their holonomic basis and orthonormal characteristics. It is established that Cartesian coordinates, defined by the basis vectors ##e_i = \delta _i^j##, possess a holonomic basis that is orthonormal throughout the entire space. The conversation emphasizes the uniqueness of Cartesian coordinates in this context, suggesting that other coordinate systems may not share these properties.

PREREQUISITES
  • Understanding of holonomic and non-holonomic systems
  • Familiarity with orthonormal basis concepts
  • Knowledge of Cartesian coordinate systems
  • Basic principles of linear algebra
NEXT STEPS
  • Research the properties of holonomic vs. non-holonomic systems
  • Explore orthonormal basis in different coordinate systems
  • Study the implications of basis transformations in linear algebra
  • Investigate other coordinate systems and their holonomic properties
USEFUL FOR

Mathematicians, physicists, and students studying advanced calculus or differential geometry who are interested in the properties of coordinate systems and their applications in various fields.

mairzydoats
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Are cartesian coordinates the only coordinates with a holonomic basis that's orthonormal everywhere?
 
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How do you define cartesian coordinates?
 
martinbn said:
How do you define cartesian coordinates?
I would assume rectangular coordinates with basis ##e_i = \delta _i^j##
 

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