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Are you ready to dive into the fascinating world of Continuum Mechanics? Look no further than Continuumech!
Our channel is dedicated to helping you self-study this exciting field with separate video lessons based on the renowned textbook Introduction to Continuum Mechanics by Lai, Rubin, and Krempl.
We'll take you through the concepts step by step, making even the most complex ideas easy to understand.
And the best part? You can learn at your own pace, whenever and wherever you want! So don't wait any longer - hit that subscribe button and join our community of Continuum Mechanics enthusiasts. Let's explore the wonders of the universe together!

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7:05

17. Representing Tensors Using Base Vectors | Dyadic Products | Continuum Mechanics | AI

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Shared 8 months ago

110 views

8:35

16. Transpose of Tensors Explained: Fundamentals & Applications | Continuum Mechanics | AI

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Shared 9 months ago

78 views

4:26

15. Understanding Tensor Representation: Matrix Form Explained with Examples | Continuum Mechanics

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Shared 9 months ago

95 views

2:28

14. How to prove that a transformation is not linear ? An Example - Continuum Mechanics

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Shared 9 months ago

38 views

7:12

13.Tensors | Exploring Sum and Product of Tensors! #tensors #tensoranalysis #tensor

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Shared 2 years ago

147 views

5:30

12. Tensors | Components of a Transformed Vector | Continuum Mechanics

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Shared 2 years ago

246 views

8:52

11. How to derive the components of a Tensor? | Continuum mechanics!

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Shared 2 years ago

413 views

7:48

10. What is a Tensor? Understanding the Basics - Continuum Mechanics

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Shared 2 years ago

1.6K views

4:10

6. Summation convention (Einstein's notation)

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Shared 2 years ago

347 views

3:16

Problem 17- Indicial manipulation

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Shared 5 years ago

31 views

3:25

Problem 16 - How to write a matrix as a sum of a symmetric and an skew-symmetric matrices.

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Shared 5 years ago

28 views

3:24

Problem15 - Indicial Manipulation

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Shared 5 years ago

16 views

3:26

Problem 14 - Indicial Manipulation

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Shared 5 years ago

39 views

2:28

Problem13

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17 views

15:52

Problem 12 - Proving an important identity

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Shared 5 years ago

28 views

4:29

Problem 11 - Indicial Manipulation

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Shared 5 years ago

34 views

5:27

Problem10 - Indicial Manipulation

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Shared 5 years ago

31 views

3:05

Problem 9 - Indicial manipulation

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Shared 5 years ago

72 views

4:57

Problem 8 - Indicial manipulation

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Shared 5 years ago

40 views

0:56

Problem 7 - The long form of an indicial equation.

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Shared 5 years ago

33 views

2:04

Problem 6 -Indicial manipulation

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Shared 5 years ago

37 views

0:57

Problem 5 - Indicial notation of expanded equations

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Shared 5 years ago

60 views

3:56

Problem 4 - four-step method to extract indicial notation of a matrix equation

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Shared 5 years ago

139 views

4:41

problem 3- Equivalence of matrix and indicial equations.

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Shared 5 years ago

49 views

4:08

9. Indicial notation manipulations: Substitution, Multiplication, Factoring, and Contraction

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Shared 5 years ago

315 views

1:24

Problem 2

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51 views

5:28

Problem1

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Shared 5 years ago

72 views

3:50

8. Vector (cross) product

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Shared 5 years ago

77 views

5:43

7. Permutation symbol

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Shared 5 years ago

377 views

6:56

6. Summation convention (Einstein's notation)

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Shared 5 years ago

437 views

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2025-12-06T12:17:19Z`
Route: `/channel/UCVdnpylkERMPRd-RoGLB0MQ`
Version: `2025.12.05-0da79a1d @ master`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /home/invidious/crystal/share/crystal/src/hash.cr:1198:9 in '??'
  from /home/invidious/crystal/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:523:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1034:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1081:14 in 'extract_items'
  from src/invidious/channels/videos.cr:32:12 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:106:14 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /home/invidious/crystal/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2025-12-06T12:17:19Z`
Route: `/channel/UCVdnpylkERMPRd-RoGLB0MQ`
Version: `2025.12.05-0da79a1d @ master`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /home/invidious/crystal/share/crystal/src/hash.cr:1198:9 in '??'
  from /home/invidious/crystal/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:523:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1034:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1081:14 in 'extract_items'
  from src/invidious/channels/videos.cr:32:12 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:106:14 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /home/invidious/crystal/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2025-12-06T12:17:19Z`
Route: `/channel/UCVdnpylkERMPRd-RoGLB0MQ`
Version: `2025.12.05-0da79a1d @ master`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /home/invidious/crystal/share/crystal/src/hash.cr:1198:9 in '??'
  from /home/invidious/crystal/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:523:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1034:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1081:14 in 'extract_items'
  from src/invidious/channels/videos.cr:32:12 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:106:14 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /home/invidious/crystal/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2025-12-06T12:17:19Z`
Route: `/channel/UCVdnpylkERMPRd-RoGLB0MQ`
Version: `2025.12.05-0da79a1d @ master`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /home/invidious/crystal/share/crystal/src/hash.cr:1198:9 in '??'
  from /home/invidious/crystal/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:523:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1034:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1081:14 in 'extract_items'
  from src/invidious/channels/videos.cr:32:12 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:106:14 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /home/invidious/crystal/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2025-12-06T12:17:19Z`
Route: `/channel/UCVdnpylkERMPRd-RoGLB0MQ`
Version: `2025.12.05-0da79a1d @ master`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /home/invidious/crystal/share/crystal/src/hash.cr:1198:9 in '??'
  from /home/invidious/crystal/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:523:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1034:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1081:14 in 'extract_items'
  from src/invidious/channels/videos.cr:32:12 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:106:14 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /home/invidious/crystal/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2025-12-06T12:17:19Z`
Route: `/channel/UCVdnpylkERMPRd-RoGLB0MQ`
Version: `2025.12.05-0da79a1d @ master`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /home/invidious/crystal/share/crystal/src/hash.cr:1198:9 in '??'
  from /home/invidious/crystal/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:523:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1034:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1081:14 in 'extract_items'
  from src/invidious/channels/videos.cr:32:12 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:106:14 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /home/invidious/crystal/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>

Unable to parse item

Invidious encountered an error while trying to parse this item. For more information see below:

Show technical details 
Title: `Missing hash key: "collectionThumbnailViewModel" (KeyError)`
Date: `2025-12-06T12:17:19Z`
Route: `/channel/UCVdnpylkERMPRd-RoGLB0MQ`
Version: `2025.12.05-0da79a1d @ master`

<details>
<summary>Backtrace</summary>
<p>
   
```
Missing hash key: "collectionThumbnailViewModel" (KeyError)
  from /home/invidious/crystal/share/crystal/src/hash.cr:1198:9 in '??'
  from /home/invidious/crystal/share/crystal/src/json/any.cr:149:5 in 'process'
  from src/invidious/yt_backend/extractors.cr:523:17 in 'process'
  from src/invidious/yt_backend/extractors.cr:1034:17 in 'parse_item'
  from src/invidious/yt_backend/extractors.cr:1081:14 in 'extract_items'
  from src/invidious/channels/videos.cr:32:12 in 'get_60_videos:continuation:sort_by'
  from src/invidious/routes/channels.cr:56:36 in 'videos'
  from lib/kemal/src/kemal/route.cr:13:9 in '->'
  from src/invidious/helpers/handlers.cr:31:37 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from lib/kemal/src/kemal/filter_handler.cr:22:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/invidious/helpers/handlers.cr:80:12 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call_next'
  from src/ext/kemal_static_file_handler.cr:106:14 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/handler.cr:30:7 in 'call'
  from /home/invidious/crystal/share/crystal/src/http/server/request_processor.cr:51:11 in 'handle_client'
  from /home/invidious/crystal/share/crystal/src/fiber.cr:170:11 in 'run'
  from ???
```
</p>
</details>